integration orthogonality trigonometric product-to-sum formula substitution special cases definite integral algebraic manipulation

Problem

No solution available for this problem.

\begin{questionparts} 
	\item
Evaluate 
\[
\int_{0}^{2\pi}\cos(mx)\cos(nx)\,\mathrm{d}x,
\]
where $m,n$ are integers, taking into account any special cases that
arise. 

\item Find ${\displaystyle \int\sqrt{1+\frac{1}{x}}\,\mathrm{d}x}.$
\end{questionparts}