Question

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

b)$\int\limits{cos\ x}\ sen^4 \, xdx$

Answer 1

a)

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

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

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

b)

$\int\limits{(cos\ x}\ sen^4 \, x)dx \\ = \frac{ {sin}^{5}x}{5} + c$