The U-sub isn't completely obvious

Calculus Level 4

E=0π/4sinx+cosx1sinxcosx+1dx \displaystyle \large \mathscr{E} = \int_{0}^{\pi/4} \dfrac{\sin x + \cos x - 1}{\sin x - \cos x + 1} \, dx

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

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