Question

Integrate
∫cos²x sinx dx
​

Answer 1

Let, cos(x) = t => -sin(x)dx = dt => sin(x)dx = -dt

`→\int { \cos}^(2)( x ).\ sin(x)dx \\ =- \int {t}^(2) dt = -\frac{ {t}^(3) }{3} + C = \boxed{ -(1)/(3) \cos^(3) (x) + C}✓`

• -1/3cos³(x)+C is the right answer.

Answer 2

-⅓ cos³ x + C

Step-by-step 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:

-⅓ cos³ x + C