# Method to solve this integral?

How could I proceed in order to solve this double integral?

$$\iint_D \frac{3+ e^{yx} -yxe^{yx}}{(3+e^{yx})^2}dxdy$$ where D is the region whose boundary is the square with vertices (0,0), (1,0), (1,1), (0,1).

I have though about change of variables, but I can only think of having u = xy, no clue for v.

All clues are appreciated.

• It sort of looks like that's the derivative of a quotient. Following through with that, we could see that the integrand is the derivative of the function $\frac{xy}{3+e^{xy}}$ with respect to $xy$. – Harry May 12 '17 at 7:48
• The boundary of a square is a closed curve (one-dimensional), and not a two-dimensional region on which one can take an area integral. So is D perhaps the square region (not its boundary) ? – Manuel Guillen May 12 '17 at 8:22
• Thanks Manuel, I will update that. I must have copied this wrong. I finally came to the conclusion that it was a quotient integral, but I was a little skeptical about not finding any other way to solve the integral. Thanks to both of you! – Bee May 12 '17 at 16:37

There is no need to set $u=xy$, because we have: