Example 2

Tag 08FO, permanent. Cite it as [Bourbaki, Tag 08FO].

The function $e^{t^2}$ is of order $+\infty$ relative to $x$ and satisfies the conditions of prop. 8, so

\int_a^x e^{t^2}\,dt \sim \frac{1}{2x}\,e^{x^2}.

In the Appendix (V, p. 252) we shall define a set of functions for which prop. 7 and prop. 8 always apply.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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