MHB Definite integral ∫(cos4x−cos4α)/(cosx−cosα)dx

[lfdahl]

Evaluate the definite integral:\[I = \int_{0}^{\pi}\frac{\cos 4x - \cos 4\alpha }{\cos x - \cos \alpha }dx\]- for some $\alpha \in \mathbb{R}.$

 

[lfdahl]

Here´s the solution (in PGN-format):

Spoiler

View attachment 7312

 

[Opalg]

[sp]It looks as though the answer should be $I = 4\pi\cos2\alpha\cos\alpha$ (because the constant is integrated over an interval of length $\pi$). (Cool)
[/sp]

 

[lfdahl]

[sp]It looks as though the answer should be $I = 4\pi\cos2\alpha\cos\alpha$ (because the constant is integrated over an interval of length $\pi$). (Cool)
[/sp]

Spoiler

Yes, indeed. A factor $\pi$ is missing in the answer. I am so sorry for this typo!