Evaluate the following integrals:

∫ cos⁵ x dx

∫ cos⁵ x dx = ∫

= ∫ { since sin²x + cos²x = 1}

= ∫

= ∫( cos (

= ∫( cos ( { since sin²x + cos²x = 1}

= ∫( cos

= ∫ cos (separate the integrals)

We know , d(sin x) = cos xdx

So put sin x = t and dt = cos xdx in above integrals

= ∫ cos

= ∫ cos

= ∫ cos

= ∫ cos

= ∫ cos

= ( since ∫xⁿ dx = + c )

Put back t = sin x

=