Well in that case, it won't work.

To reverse integration order, we rewrite the double integral as

Now play with inequalities: Hence After reversing integration order the double integral equals which is doable. (Only the inner one.)

But we have a problem, that will yield another undoable integral which result is exactly so the only way to tackle this, it's a power series application.

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If you want to try a double integral trick, see You can watch my solution here.