The integral is .

Asssume .

Differentiate on each side.

Substitute and in the integral.

Double angle formula : .

Replace in above expression.

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Apply double angle formula: .

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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 .

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Graph :

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