Integral involving exponential logarithm

[cielo]

Homework Statement

If X is a random variable with density function: f(x) = \lambdae^{-x \lambda}where X>=0.

Homework Equations

Why is the expected value of X, or E[X] = \frac{1}{\lambda}?

The Attempt at a Solution

E[X] = \int x*(\lambdae^{- \lambda}^{x}) dx, where the integral is from 0 to infinity.

I let u = -\lambdax
du = -\lambda dx

but I can't get the \frac{1}{\lambda} as the answer when I performed the integration.

 

[HallsofIvy]

If you let u= \lambda x then x= u/\lambda and the integral becomes
\int \frac{u}{\lambda}e^{-u} du= \frac{1}{\lambda}\int ue^{-u}du

Did you remember to replace the "x" multiplying the exponential with u/\lambda?