Formula to be used – We know , cos3x = 4cos³x-3cosx

Assuming x = cosa, 4cos³a-3cosa=cos3a

And, dx = -sinada

Hence, a=cos^-1x

Again, sina=√(1-x²)

Tip – If f₁(x) and f₂(x) are two functions , then an integral of the form can be INTEGRATED BY PARTS as

where f₁(x) and f₂(x) are the first and second functions respectively.

Taking f₁(x) = a and f₂(x) = sina,

Replacing the value of a we get,

, where c is the integrating constant