# That pesky 1

Calculus Level 4

$\large \displaystyle \int_{0}^{\pi/2} \dfrac{\sin x + 1}{\sin x + \cos x} \, dx$

If the above integral can be expressed in the form $\dfrac{\pi}{a} + \cos \left( \dfrac{ \pi }{b}\right) \ln \left( \dfrac{\sqrt{c }+ d}{\sqrt{c} - d} \right) ,$

where $$a, b, c$$ and $$d$$ are positive integers, with $$c$$ square-free, find $$a + b + c + d$$.

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