Question

Calcule $\int\limits {cos^2} \,5 xdx$

Answer 1

$∫ {cos}^{2} (5x)dx \\ = \frac{1}{2} ∫(1 + cos(10x))dx \\ = \frac{1}{2} ∫dx \: + \frac{1}{2} ∫ \cos(10x)dx$

$\frac{1}{2} x + \frac{1}{2} . \frac{1}{10} \sin(10x) + c \\ = \frac{1}{2} x + \frac{1}{20} \sin(10x) + c$