Just another Integral

Calculus Level 4

Find \(a + b\) if

\[\large \int_{0}^{2017}{\frac{e^{\cos(\{x\}\pi)}}{e^{\cos(\{x\}\pi)} + e^{-\cos(\{x\}\pi)}}} dx = \frac ab \]

Notes:

  • \(\gcd{(a,b)} = 1\)
  • \(\{x\}\) denotes the fractional part of \(x\).
  • \(e\) is the Euler's number (\(\approx 2.71828...\))
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