Let's do some calculus! (22)

Calculus Level 4

π/2π/2esinxcosx1+etanxdx = ?\large \displaystyle \int_{{-\pi}/{2}}^{{\pi}/{2}} {\dfrac{ e^{\left| \sin x \right|} \cos x}{1 + e^{\tan x}}} \,dx ~ = ~ ?

Notations: e2.718e \approx 2.718 is the Euler's number. For your answer take this approximate value as the value of ee.


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