Chapter 14.7, Problem 38ES

Evaluate the integral by making an appropriate change of variables.

${\displaystyle \underset{R}{\iint }{e}^{\left(y-x\right)/\left(y+x\right)}dA},$ where R is the region in the first quadrant enclosed by the trapezoid with vertices $\left(0,1\right),\left(1,0\right),\left(0,4\right),\left(4,0\right).$