Primitive of x squared by Exponential of x/Proof 1

Theorem

$\ds \int x^2 e^x \rd x = e^x \paren {x^2 - 2 x + 2} + C$

Proof

From Primitive of $x^2 e^{a x}$:

$\ds \int x^2 e^{a x} \rd x = \frac {e^{a x} } a \paren {x^2 - \frac {2 x} a + \frac 2 {a^2} } + C$

The result follows by setting $a = 1$.

$\blacksquare$