g(x) = ∫(1~x²) cosx/x dxg'(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/...