The U-sub isn't completely obvious

Calculus Level 4

\[ \displaystyle \large \mathscr{E} = \int_{0}^{\pi/4} \dfrac{\sin x + \cos x - 1}{\sin x - \cos x + 1} \, dx \]

If \( \mathscr{E} \) can be represented in the form \( \ln \left(a + \dfrac{b}{\sqrt{c}} \right) \), where \(a,b\) and \(c\) are integers with \(c\) square-free, find \(a+b+c\).

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