Evaluate:
Question:

Evaluate: $\int \cos ^{2} n x d x$

Solution:

We know, $\cos ^{2} x=\frac{1+\cos 2 x}{2}$

$\therefore$ The given equation becomes,

$\Rightarrow \int \frac{1+\cos \mathrm{n} \mathrm{x}}{2} \mathrm{dx}=\int \frac{1+\cos 2 \mathrm{nx}}{2} \mathrm{dx}$

We know $\int \cos \mathrm{ax} \mathrm{dx}=\frac{1}{\mathrm{a}} \sin \mathrm{ax}+\mathrm{c}$

$\Rightarrow \frac{1}{2} \int d x+\frac{1}{2} \int \cos (2 n x) d x$

$\Rightarrow \frac{x}{2}+\frac{1}{4 n} \sin (2 n x)+c$

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