Optimal. Leaf size=14 \[ \frac{2 \sqrt{a+b x}}{b} \]
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Rubi [A] time = 0.0013685, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {32} \[ \frac{2 \sqrt{a+b x}}{b} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{a+b x}} \, dx &=\frac{2 \sqrt{a+b x}}{b}\\ \end{align*}
Mathematica [A] time = 0.0034517, size = 14, normalized size = 1. \[ \frac{2 \sqrt{a+b x}}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \begin{align*} 2\,{\frac{\sqrt{bx+a}}{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.939872, size = 16, normalized size = 1.14 \begin{align*} \frac{2 \, \sqrt{b x + a}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.61068, size = 26, normalized size = 1.86 \begin{align*} \frac{2 \, \sqrt{b x + a}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.054909, size = 10, normalized size = 0.71 \begin{align*} \frac{2 \sqrt{a + b x}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06621, size = 16, normalized size = 1.14 \begin{align*} \frac{2 \, \sqrt{b x + a}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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