# Solving a non-exact differential

I started off solving the differential equation $$(xy^2 + 3e^{x-3})dx - x^2ydy = 0$$ It's a non-exact first order equation whose integrating factor is $1/x^4$.

Finally I got to the equation where I needed to integrate $$\frac{e^{x-3}}{x^4} dx$$ But I can't seem to proceed. Is there any other way to solve this.

• Not in terms of elementary functions. – Chris K May 12 '14 at 12:45