Question

Find the integrals (primitives):
$\rm \displaystyle\int \cos^{2}x \ dx$

Answer 1

We know that

${cos}^{2} x = \frac{1 + cos \: 2x}{2}$
$\int \cos^{2}x \ dx = \int \: \frac{1 + cos \: 2x}{2}dx$
apply linearity

$\int \: \frac{1}{2} dx + \int \: \frac{cos \: 2x}{2} dx \\ \\ \frac{1}{2} \int \: 1 \: dx + \frac{1}{2} \int \: cos \: 2x \: dx \\ \\ \int \cos^{2}x \ dx = \frac{x}{2} + \frac{1}{4} sin \: 2x + C$
Hope it helps you.