Integral of $e^{\frac{y}{x}}$ How can we evaluate the following?

$$\int e^{\frac{y}{x}}\ \mathrm dy$$

An explanation of the answer would be helpful.

The answer I got is $ x  e^{y/x}$.

But not sure about the steps used for obtaining the answer...
Since this a task on finding a primitive, you can always check you candidate answer by taking (partial in your case) derivative.
First note that
$$\int a^t\ \mathrm dt=\frac{a^t}{\ln a}+C$$
Therefore
$$\int e^{\frac{y}{x}}\ \mathrm dy=\int \left(e^{\frac{1}{x}}\right)^y\ \mathrm dy$$
$$=\frac{\left(e^{\frac{1}{x}}\right)^y}{\ln e^{\frac{1}{x}}}+C=xe^{\frac{y}{x}}+C$$