Find the improper integral of te^-st dt from 0 to b where the limit of b approaches to positive infinity.
Use integration in parts
∫0b t e-st dt = -(1/s) t e-st (from o to b) + (1/s)∫0b e -st dt = -(b/s) e -sb - (1/s2) e -sb (from 0 to b) =
-(b/s)e - sb - (1/s2) e -sb + 1/s2
Now, if you take limes b →∞ you will get: ∫ = 1/s2 (answer)