# What is the value of $\int_{0}^{a} \int_{0}^{x} \frac{x}{y} \cosh{y} \; dy \, dx$?

I had the following double integral in my recent math examination:

$$\int_{0}^{a} \int_{0}^{x} \frac{x}{y} \cosh{y} \; dy \, dx$$ where $$a \in \mathbb{R}$$

I tried changing the order of the integrals, however that didn't help much. Here's what I've got after changing the order:

$$\int_{0}^{a} \int_{y}^{a} \frac{x}{y} \cosh{y} \; dx \, dy$$

In both cases I tried integration by parts, however I couldn't solve the resulting integrals. I'm beginning to think that there might have been an error and the actual task should have been:

$$\int_{0}^{a} \int_{x}^{a} \frac{x}{y} \cosh{y} \; dy \, dx$$

In this case, if I change the order of integration the resulting integral can be easily solved.

I would much appreciate any help. Thanks in advance.

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Maybe it should be $\sinh$? –  Jon Claus May 24 '13 at 19:28