Optimal. Leaf size=12 \[ e^{a+b x+c x^2} \]
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Rubi [A] time = 0.0192453, antiderivative size = 12, 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 = {2236} \[ e^{a+b x+c x^2} \]
Antiderivative was successfully verified.
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Rule 2236
Rubi steps
\begin{align*} \int e^{a+b x+c x^2} (b+2 c x) \, dx &=e^{a+b x+c x^2}\\ \end{align*}
Mathematica [A] time = 0.0373032, size = 12, normalized size = 1. \[ e^{a+b x+c x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.036, size = 12, normalized size = 1. \begin{align*}{{\rm e}^{c{x}^{2}+bx+a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.974464, size = 15, normalized size = 1.25 \begin{align*} e^{\left (c x^{2} + b x + a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.706163, size = 28, normalized size = 2.33 \begin{align*} e^{\left (c x^{2} + b x + a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.100673, size = 10, normalized size = 0.83 \begin{align*} e^{a + b x + c x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.25708, size = 15, normalized size = 1.25 \begin{align*} e^{\left (c x^{2} + b x + a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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