Question

\[\int \cos^2 \text{nx dx}\]

Answer 1

\[\int \cos^2 \text{nx dx}\]
\[ = \int\left[ \frac{1 + \cos 2nx}{2} \right] dx \left[ \therefore \cos^2 x = \frac{1 + \cos 2x}{2} \right]\]
\[ = \frac{1}{2}\int\left( 1 + \cos 2nx \right)dx\]
\[ = \frac{1}{2}\left[ x + \frac{\sin 2nx}{2n} \right] + C\]
\[ = \frac{x}{2} + \frac{\sin 2nx}{4n} + C\]