Answer:
-⅓ cos³ x + C
Explanation:
∫ cos² x sin x dx
If u = cos x, then du = -sin dx.
∫ -u² du
Integrate using power rule:
-⅓ u³ + C
Substitute back:
Let, cos(x) = t => -sin(x)dx = dt => sin(x)dx = -dt
[tex] →\int { \cos}^{2}( x ).\ sin(x)dx \\ =- \int {t}^{2} dt = -\frac{ {t}^{3} }{3} + C = \boxed{ -\frac{1}{3} \cos^{3} (x) + C}✓[/tex]
