How to integrate x^2*ln(x)?

To integrate x^2*ln(x), use integration by parts with u = ln(x) and dv = x^2 dx.

To integrate x^2*ln(x), we can use integration by parts. Let u = ln(x) and dv = x^2 dx. Then du/dx = 1/x and v = (1/3)x^3. Using the formula for integration by parts, we have:

∫ x^2 ln(x) dx = u*v - ∫ v du/dx dx
= ln(x) * (1/3)x^3 - ∫ (1/3)x^3 * (1/x) dx
= (1/3)x^3 ln(x) - (1/9)x^3 + C

Therefore, the antiderivative of x^2*ln(x) is (1/3)x^3 ln(x) - (1/9)x^3 + C, where C is the constant of integration.