Trying to find a way to solve 

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> $$\int\_{-\infty}^\infty \frac{1}{x^8+1}dx$$ 
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through Glasser's Master Theorem, more specifically the Cauchy–Schlömilch substitution. Preferably, I'm looking for the closed form solution, and I am already aware of how to attain this through contour integration. 

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> Solution: $$\frac{\pi}{4\sin(\frac{\pi}{8})}$$ 
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Link to general closed form solution: [solutions to $\int\_{-\infty}^\infty \frac{1}{x^n+1}dx$ for even $n$](https://math.stackexchange.com/questions/3035999/solutions-to-int-infty-infty-frac1xn1dx-for-even-n#comment6260072_3035999)