An amazing Integral

Calculus Level 5

Evaluate the following integral

011+x2017dx\displaystyle \large \int_{0}^{\infty} \dfrac{1}{1+x^{2017}} \, dx

If your answer comes in the form of πabcsc(πc)\dfrac{\pi^a}{b} \csc \left(\dfrac{\pi}{c}\right) where a,b,ca,b,c are positive integers then submit your answer as a+b+ca+b+c.

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