Answer:
sin(x)−1/3(sin3(x))+C
Step-by-step explanation:
use u substitution method to integrate
cos³(x) = cos(x) cos²(x)
… = cos(x) (1 - sin²(x))
Substitute u = sin(x) and du = cos(x) dx. Then in the integral, you get
∫ cos³(x) dx = ∫ (1 - u ²) du
… = u - 1/3 u ³ + C
… = sin(x) - 1/3 sin³(x) + C
