Tuesday, 29 October 2013

calculus - Tangent half-angle substitution for int2pi0frac1cosx3+cosx

I want to evaluate the following integral using the tangent half-angle substitution t=tan(x2): 2π01cosx3+cosx dx However, making the substitution gives me 0 for each of the limits of integration, which is obviously incorrect. I know that one way to solve this problem is to notice that, by symmetry, the equivalent integral 2π01cosx3+cosx dx allows the subsitution to work. What are ways to make this substitution work without noticing this symmetry? I know that this general question has been asked on here before, but I am specifically interested in how I can make it work with this substitution.

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