g(x) = ∫(1~x²) cosx/x dx
g'(x) = 2x * cos(x²)/(x²) = [2cos(x²)]/x
∫(0~1) xg(x) dx
= ∫(0~1) g(x) d[x²/2]
= [x²/2]g(x) |(0~1) - [1/2]∫(0~1) x²g'(x) dx
= [1/2]g(1) - [1/2]∫(0~1) x² * [2cos(x²)]/x dx
= - ∫(0~1) xcos(x²) dx
= [- 1/2]∫(0~1) cos(x²) d(x²)
= [- 1/2][sin(x²)] |(0~1)
= [- 1/2][sin(1) - 0]
= (- 1/2)sin(1)