Optimal. Leaf size=16 \[ \frac{2 \sqrt{e^{a+b x}}}{b} \]
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Rubi [A] time = 0.0065371, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {2194} \[ \frac{2 \sqrt{e^{a+b x}}}{b} \]
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin{align*} \int \sqrt{e^{a+b x}} \, dx &=\frac{2 \sqrt{e^{a+b x}}}{b}\\ \end{align*}
Mathematica [A] time = 0.0050288, size = 16, normalized size = 1. \[ \frac{2 \sqrt{e^{a+b x}}}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 0.9 \begin{align*} 2\,{\frac{\sqrt{{{\rm e}^{bx+a}}}}{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04315, size = 19, normalized size = 1.19 \begin{align*} \frac{2 \, e^{\left (\frac{1}{2} \, b x + \frac{1}{2} \, a\right )}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46732, size = 34, normalized size = 2.12 \begin{align*} \frac{2 \, e^{\left (\frac{1}{2} \, b x + \frac{1}{2} \, a\right )}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.082823, size = 14, normalized size = 0.88 \begin{align*} \begin{cases} \frac{2 \sqrt{e^{a + b x}}}{b} & \text{for}\: b \neq 0 \\x & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.24524, size = 19, normalized size = 1.19 \begin{align*} \frac{2 \, e^{\left (\frac{1}{2} \, b x + \frac{1}{2} \, a\right )}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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