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u = ln x²
du = 2/x dx
dv = x dx
v = (1/2).x²
∫ x.ln x² dx = u.v - ∫ v.du
= (1/2).x².ln x² - ∫ (1/2).x².(2/x) dx
= (1/2).x².ln x² - ∫ x dx
= (1/2).x².ln x² - (1/2).x²
= (1/2).x².(ln x² - 1)