H2 Maths 5.3 - Integration by Parts: ∫ x² ln x dx

What you will learn

• Find integral of x^2 ln x dx using integration by parts: integral u dv = u v - integral v du.
• LIATE: log beats algebra, so u = ln x and dv = x^2 dx; du = (1/x) dx and v = x^3 / 3.
• Substitute: integral = (x^3 / 3) ln x - (1/3) integral x^2 dx = (x^3 / 3) ln x - x^3 / 9 + C.