I have the problem of (ylny + e^x)dx + (x+e^-y + xlny)dy. I have determined that they are exact. However, I am running into a problem when I am trying to solve the equation. I have done the following and got stuck!

1. partial F with respect to x = ylny + e^x and

2. partial F with respect to y = x + e^-y + xlny

When I integrated #1 with respect to x, I came up with: xylny + e^x + g(y) and then when I integrated #2 with respect to y, I came up with:

xy - e^-y + xylny -x + h(x). From here I am stuck, therefore I think I made a mistake somewhere and I can't seem to find it. Can somebody help?