Integrating Factorials

Question

I feel like I'm doing something wrong here: $$\frac{d^n}{dx^n}(x^n)=n!$$

$$ 5!=\frac{d^5}{dx^5}(x^5)$$

$$ \int{5! dx}=\int{\frac{d^5}{dx^5}(x^5)}dx=x\frac{d^4}{dx^4}(x^4)=x*4!$$

Please explain what I'm doing wrong.

Answer 1

$$ \int{5! dx}=\int{\frac{d^5}{dx^5}(x^5)}dx=\frac{d^4}{dx^4}(x^5)=x*5!$$

$$ \int 120 dx = 120*x$$

*Thanks Cocopuffs

Answer 2

$ \int{5! dx}=\int{\frac{d^5}{dx^5}(x^5)}dx=5\frac{d^4}{dx^4}(x^4)=5*4! $