$\int_{-\infty}^{0}xe^{x}$ diverge or converge How would one find whether the following improper integral converge or diverge.
$\int_{-\infty}^{0}xe^{x}$
I did the following.
$t\rightarrow\infty$
$\int_{t}^{0}xe^x$
I did the integration by parts.
$u=x$
$dv=e^x$
$xe^x-\int 1e^x$
$xe^x-1xe^x$
$(0)(e^0)-e^0(0)-te^t-te^t$
$0-\infty-\infty$
would this mean there is a divergence.

Step 1: set the limit $\lim_{t \rightarrow -\infty} $
Step 2: find integral (i got $xe^x - e^x$)
Step 3: plug in the limits and  ftc, so u get 
$\lim_{ t-> -\infty} [(0-e^0)-(te^t-e^t)]$
*key: $e^\infty = \infty$,
$e^-\infty = 0$
step 4: evaluate 
answer: convergent sum $-1 $
