What is integral of x ln x dx

u= ln x
dv=x dx
please help...

u = ln(x)
du = dx / x
dv = x * dx
v = (1/2) * x^2

int(u * dv) = u * v - int(v * du)

(1/2) * x^2 * ln(x) - int((1/2) * x^2 * dx / x) =>
(1/2) * x^2 * ln(x) - (1/2) * int(x * dx) =>
(1/2) * x^2 * ln(x) - (1/2) * (1/2) * x^2 + C =>
(1/4) * x^2 * (2 * ln(x) - 1) + C