What's the integral of x*ln(x)?

The integral of x*ln(x) is (x^2/2)*ln(x) - (x^2/4) + C.

To solve this integral, we can use integration by parts. Let u = ln(x) and dv = x dx. Then du = (1/x) dx and v = (x^2/2). Using the formula for integration by parts, we have:

∫ x*ln(x) dx = uv - ∫ v du
= (x^2/2)*ln(x) - ∫ (x^2/2) * (1/x) dx
= (x^2/2)*ln(x) - ∫ (x/2) dx
= (x^2/2)*ln(x) - (x^2/4) + C

Therefore, the integral of x*ln(x) is (x^2/2)*ln(x) - (x^2/4) + C.