Evaluate the following integrals:

∫ sin5 x dx

∫ sin5 x dx = ∫


= { since sin2x + cos2x = 1}


=


= ∫( sin (


= ∫( sin ( { since sin2x + cos2x = 1}


= ∫( sin


= ∫ sin (separate the integrals)


We know , d(cos x) = -sin xdx


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


= ∫ sin


= ∫ sin


= ∫ sin


= ∫ sin


= ∫ sin


= ( since ∫xⁿ dx = + c )


Put back t = cos x


=


=


= -[


2