Seems too easy! -2

Calculus Level 5

The value of 0π4esecxsin(x+π4)(1sinx)cosxdx\int_{0}^{\frac{\pi}{4}} e^{\sec x} \dfrac{\sin\Big( x + \dfrac{\pi}{4}\Big)}{(1 - \sin x) \cos x} dx

can be expressed as (a+b)eced.\dfrac{(a + \sqrt{b})e^{\sqrt{c}} - e}{\sqrt{d}}.

Find a+b+c+d.\displaystyle{a+b+c+d}.

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