U Substitution for an exponential distribution

Use u-substitution to evaluate the definite integral

Define u=-3x

Substitute the bounds of the integral, 0 and \infty, for x to get the new bounds, 0 and -\infty.

\frac{du}{dx} = -3 so dx = -\frac{1}{3}du

Substitute the new bounds and dx to get the new integral:

-\frac{1}{3}\int_0^{-\infty} e^{u} \, du =-\frac{1}{3}e^u\Big|_{0}^{-\infty}=0-(-\frac{1}{3})=\frac{1}{3}