I am a newbie in Mathematica. Recently, I want to use Mathematica to help my mathematics calculation.
I have the following function:
f[x_,t_]=A E^(-a Abs[x])E^(-I b t), in which A, a, b are real positive numbers.
And I would like to calculate the following integration:
Integrate[f[x,t], {x, -Infinity, Infinity}]
However, as I know A, a, b are real positive numbers, so I expect the following result:
(2 A E^(-I b t))/a
But, Mathematica give the following result:
(2 A E^(-I b t))/a, when Re[a] > 0;
Integrate[A E^(-I b t - a Abs[x]), {x, -\[Infinity], \[Infinity]}, Assumptions -> Re[a] <= 0], True
My problem is: how to let Mathematica know, A, a, b are real positive numbers, so that it could generate the result I want?
I know, this might be a simple question, but I have searched a lot of pages, and got no answer. Could anybody help me? Thanks a lot.