- #1

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Show that:

[itex]\int_0^1\int_x^1e^\frac{x}{y}dydx[/itex]=[itex]\frac{1}{2}[/itex](e-1)

I've tried reversing the order of integration then solving from there:

[itex]\int_0^1\int_y^1 e^{\frac{x}{y}}dxdy[/itex]

=[itex]\int_0^1[ye^\frac{x}{y}]_y^1dy[/itex]

=[itex]\int_0^1ye^\frac{1}{y}-ye^1dy[/itex]

But I can't integrate [itex]ye^\frac{1}{y}[/itex]

So either I've done something wrong when changing the order of integration or something else but I can't see how to go on from here.

Thanks,

Chris.