Improper Integrals: Example 2: x*e^x

In this video I go over another example on improper integrals and this time solve the integral of the function x*e^x from x = -∞ to x = 0. In solving this improper integral, I had to use the method of integration by parts as well as the L'Hospital's Rule for evaluating the resulting limit and show that this function does in fact converge and the answer is simply -1.

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I don't always evaluate improper integrals but when I do I usually need to use L'Hospital's Rule in solving it ;)