Integration of $e^{-x}$ with respect to y

Question

I'm not sure if I'm being incredibly stupid and having a brain dead moment! any help is appreciated!

The question I'm referring to is dealing with the integration of an exponential function of x with respect to y, but i think it would be more beneficial to understand the more simple $$\int{e^{-x} dy}$$ before attempting a complex integration. Thank you!

Answer 1

Hint: $e^{-x}$ is constant with respect to $y$. So how do you integrate a constant?

Another hint: for any constant $c$ we have $\int c\,dy=cy+C$.

Answer: Finally we have $\int e^{-x}\,dy=ye^{-x}+C$.

Answer 2

This is very simple. Irrespective of the number of variables in the integrand only the variable with respect to which integration is being done will be considered a variable and the others will be deemed constants. Hence we have $$\int{e^{-x} dy}=e^{-x}y + c$$