Optimal. Leaf size=14 \[ \frac{2 \sqrt{c+d x}}{d} \]
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Rubi [A] time = 0.0013672, 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} \[ \frac{2 \sqrt{c+d x}}{d} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{c+d x}} \, dx &=\frac{2 \sqrt{c+d x}}{d}\\ \end{align*}
Mathematica [A] time = 0.0033623, size = 14, normalized size = 1. \[ \frac{2 \sqrt{c+d x}}{d} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \begin{align*} 2\,{\frac{\sqrt{dx+c}}{d}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.946391, size = 16, normalized size = 1.14 \begin{align*} \frac{2 \, \sqrt{d x + c}}{d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.77387, size = 26, normalized size = 1.86 \begin{align*} \frac{2 \, \sqrt{d x + c}}{d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.05371, size = 10, normalized size = 0.71 \begin{align*} \frac{2 \sqrt{c + d x}}{d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0456, size = 16, normalized size = 1.14 \begin{align*} \frac{2 \, \sqrt{d x + c}}{d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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