Let's go back a couple years

Calculus Level 3

π/2π/212007x+1sin2008xsin2008x+cos2008xdx=? \large \int_{-\pi/2}^{\pi /2} \dfrac1{2007^x + 1} \cdot \dfrac{\sin^{2008} x}{\sin^{2008}x + \cos^{2008} x} \, dx = \, ?

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