# How do you integrate f(x)=e^(-x^2)/x using the quotient rule?

The quotient rule is used to differentiate a function of the form $y \left(x\right) = \frac{P \left(x\right)}{Q \left(x\right)}$. There is no such thing as a quotient rule for integration.
There is no elementary indefinite integral for $\int \setminus {e}^{- {x}^{2}} / x \setminus \mathrm{dx}$