My eleventh integral problem

Calculus Level 5

0π/2excos2xdx \large \displaystyle \int_{0}^{\pi/2} e^{x} \cos^{2} x \, dx

It is given that the above integral can be expressed in the form aebπ/cdf\large \dfrac{a e^{{b \pi}/{c}}-d}{f} where a,b,c,d,f a, b, c, d, f are positive integers, gcd(a,f)=gcd(b,c)=1\gcd(a,f) = \gcd(b,c) = 1.

Find the value of a+b+c+d+fa+b+c+d+f.

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