integral 2x sin (3x -1) dx (persial)

Integration by Parts.

∫ 2x sin (3x - 1) dx = 2 ∫ x sin (3x - 1) dx
∫ u dv = uv - ∫ v du
u = x → du = dx
dv = sin (3x - 1) → v = -1/3 cos (3x - 1)
= -2[1/3 x cos (3x - 1) + ∫ 1/3 cos (3x - 1) dx]
= -2[1/3 x cos (3x - 1) + 1/9 sin (3x - 1)] + C
= 2/9 sin (3x - 1) - 2/3 x cos (3x - 1) + C