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[tex]f(t)=e^{i.t}[/tex]

I have to solve this equation:

[tex]\int_{0}^{\infty}e^{i.t}.e^{-s.t}dt[/tex]

If I do like this, it's very simple:

[tex]\int_{0}^{\infty}e^{i.t}.e^{-s.t}dt=\int_{0}^{\infty}e^{-t.(s-i)}dt=\frac{-1}{s-i}.(0-1)=\frac{1}{s-i}[/tex]

But, if I do like this, I can't solve it:

[tex]\int_{0}^{\infty}e^{i.t}.e^{-s.t}dt=\int_{0}^{\infty}e^{t.(i-s)}dt=\frac{1}{i-s}.(?? - 1)= ?? [/tex]

Where it says '??', I don't know what to write.

Any help? Thanks!