Integrate x*ln(x)

Let u = ln(x) and dv/dx = x

Thus du/dx = 1/x and v = x²/2

Using the formula:

Integral of udv/dx = uv - Integral of v*du/dx

This becomes: Integral of x*ln(x) = (x²ln(x))/2 - Integral of x/2

Completing the integral on the RHS gives the answer to the question: (x²ln(x))/2 - x²/4