I'm trying to use Wolfram Alpha to symbolically evaluate an integral, and I'm getting this:

integral A e^(-j sqrt(x^2+y^2)) cos(tan^(-1)(x, y)) dx = -(A e^(-j sqrt(x^2+y^2)))/j+constant

Since the purpose of the cos(tan^(-1)(x, y)) is to convert an otherwise directionless distance interaction into an x-vector, the result when integrated should still be sensitive to the sign of x. However, the result of the integration has rendered the sign of x meaningless.

Unfortunately I don't have a membership, so I can't see a breakdown of why exactly Wolfram Alpha thinks that this is the correct result.

Am I missing something, or have I stumbled across a bug?