∫[0..1] x²cos2xdx
=∫[0..1] x²/2 d(sin2x)
=sin2x * x²/2 |[0..1] - ∫[0..1] sin2x d(x²/2)
=1/2 sin2 - ∫[0..1] x sin2x dx
=1/2 sin2 + ∫[0..1] x/2 d(cos2x)
=1/2 sin2 + x/2 cos2x |[0..1] - 1/2 ∫[0..1] cos2x dx
=1/2 sin2 + 1/2 cos2 - 1/4 sin2x |[0..1]
=1/4 sin2 + 1/2 cos2