Nasty Integral

[VBAhack]

This one has me baffled:

∫e^{-√(x2 + a2)}dx

I made the obvious substitution:

y = √(x² + a²)

and came up with:

∫dy y e^-y/√(y² - a²)

Integrating by parts results in:

e^-y√(y² - a²) + ∫e^-y dy √(y² - a²)

and got stuck. Any ideas?