What is ∫_{-1}^{1} (3 sin x - sin 3x) cos² x dx equal to?

The integrand is (3 sin x - sin 3x) cos² x. Both 3 sin x and sin 3x are odd functions of x, and cos² x is an even function. The product of an odd function and an even function is odd. The integral of an odd function over a symmetric interval [-1, 1] is zero. Therefore the value of the integral is 0.