# Let's do some calculus! (22)

Calculus Level 4

$\large \displaystyle \int_{{-\pi}/{2}}^{{\pi}/{2}} {\dfrac{ e^{\left| \sin x \right|} \cos x}{1 + e^{\tan x}}} \,dx ~ = ~ ?$

Notations: $$e \approx 2.718$$ is the Euler's number. For your answer take this approximate value as the value of $$e$$.