Integrate x*ln(x) with respect to x

First identify that integration by parts is required. Then seperate the integration so u = ln(x)     dv/dx = x then, du/dx = 1/x  v = (1/2)x^2 . And using the integration by parts formula with these substitutions: ∫x*ln(x) dx = ((1/2)x^2)*ln(x)- ∫(1/2)x dx = ((1/2)x^2)*ln(x)- (1/4)x^2 +c