f(x)={1/5 e^-x/5 x>0

{0 otherwise

Determine the mean length=E(X) of this type of telephone conversation.

Here is the work I did:

Integration by parts where: u=x dv=e^-x/5 dx

du=dx v=-5e^-x/5

E(X)= -∞ ∫ ∞ xf(x) <-- where integrated from -∞ to ∞

=1/5 0 ∫ ∞ xe^-x/5 dx<-- integrated from 0 to ∞

=-1/5 xe^-x/5 - ∫-5e^-x/5 dx

=-1/5 xe^-x/5 + 5 ∫ e^-x/5 dx

=-1/5 xe^-x/5 + ∫ e^u du

=-1/5 xe^-x/5 - e^-x/5 0|∞