Integral of the product $x^n e^x$ I would be very pleased if you could give me your opinion about this way of integrating the following expression. I think that it has no issues, but just wanted to confirm:
$$ \int x^n e^x dx $$
$$ e^x = u $$
$$ e^x dx = du $$
$$ \int x^n e^x dx = \int \ln(u)^n du = nu(\ln(u) - 1) + C $$
$$ \int x^n e^xdx = ne^x (x-1) + C $$
Many thanks!

If you have an integral of the form $$\int f(x)g(x)dx$$ such that $\exists\ n \in \mathbb{N}$ for which $$\frac{d^nf(x)}{dx^n}=0$$ 
And the repeated integral of $g(x)$ is easy to compute (as is the case for exponentials), it is convenient to apply the Tabular Method for integration by parts and then proceed by induction.
