Integrate $\int\limits_{0}^{1} \frac{\log(x^{2}-2x \cos a+1)}{x} dx$ How do I solve this: $$\int\limits_{0}^{1} \frac{\log(x^{2}-2x \cos{a}+1)}{x} \ dx$$
Integration by parts is the only thing which I could think of, clearly that seems cumbersome. Substitution also doesn't work.

Please see $\textbf{Problem 4.30}$ in the book: ($\text{solutions are also given at the end}$)


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*$\text{The Math Problems Notebook,}$ by Valentin Boju and Louis Funar.
