Option for generating conditions in results
GenerateConditions
FourierTransform[E ^ (a t ^ 2), t, ω, GenerateConditions -> True]
→ FourierTransform[E^(a*t^2), t, ω, GenerateConditions -> True]Integrate[E ^ (a x), {x, 0, Infinity}, GenerateConditions -> False]
→ -a^(-1) + E^(a*Infinity)/a