# 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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