Question

Integrate e^(x/y) dx and Integrate e^(x/y) dy

Answer 1

What happens when you integrate \(e^{kx}\)? $$\int e^{kx}\,\mathrm{d}x=\frac1ke^{kx}+C$$Here, \(\dfrac1y\) is a constant w.r.t. \(x\) just like \(k\).

Answer 2

The latter is like $$\int e^{\frac1x}\,\mathrm{d}x$$which has no elementary representation... it can be written in terms of the http://en.wikipedia.org/wiki/Exponential_integral after integrating by parts.

Answer 3

Is the reason why you can't put ln up there is because it would cancel out the entire e?