The integral is .

Asssume .

Differentiate on each side.

Substitute  and  in the integral.

Double angle formula : .

Replace  in above expression.

Apply double angle formula: .

.

Consider the antiderivative function by taking  as  .

Graph :

Graph the integrand function  and its antiderivative .

Observe the graph,

When  is negative, then  is decreasing and  is positive, then  is increasing.

Hence the curve  is derivative of the curve .

Therefore,  is antiderivative of the integrand function .

.

Graph :

.