I have the double integral:
$$ \int_0^1 \int_0^{1-x} e^{\frac {y}{(x+y)}} \;dy\; dx $$
Ignore any difficulty this integral may have at the origin.
I was given a hint to simplify the exponent by taking it as a chunk. I thus set $v=\frac{y}{(x+y)}$, but am not sure what to do for you and go from there?
Can someone please help? Thanks!
HINT:
Put $x+y=v$ and $y=u$ .Now using Jacobian $ dx dy=du dv$ .
And look the new region ...
https://www.desmos.com/calculator/8cqzfvavn9
NOTE: take $u$-axis in place of $x$-axis .