Question

integration by parts of x^2 * e^x

Answer 1

let u = x^2 so du = 2x
let dv = e^x so v = e^x

INT x^2 e^x dx = uv - INT v du
= x^2 e^x - INT 2x e^x dx
INT 2x e^x dx = 2x e^x - INT 2 e^x dx
= 2x e^x - 2e^x

finally INT x^2 e^x = x^2 e^x -( 2x e^x - 2 e^x)
= e^x(x^2 -2x + 2) + c