Answer
First split up the integral into two improper integrals with only one badly-behaved limit each:
![](https://media1.shmoop.com/images/calculus/calc_indefint_improper_latek_139.png)
Now work out each of those improper integrals.
![](https://media1.shmoop.com/images/calculus/calc_indefint_improper_latek_140.png)
Since c is approaching -∞, the quantity ec is approaching 0. So
![](https://media1.shmoop.com/images/calculus/calc_indefint_improper_latek_141.png)
Now for the other integral.
![](https://media1.shmoop.com/images/calculus/calc_indefint_improper_latek_142.png)
This limit diverges. Since one of the two improper integrals diverges, the original integral diverges also.
If we had chosen to evaluate the integral
![](https://media1.shmoop.com/images/calculus/calc_indefint_improper_latek_143.png)
first, we wouldn't have had to bother with the other one at all. If we had only drawn a picture of the function first, we could have seen from the graph that
![](https://media1.shmoop.com/images/calculus/calc_indefint_improper_latek_144.png)
would diverge! The moral of the story: look at the graph of the function before you start integrating.
![](https://media1.shmoop.com/images/calculus/calc_indefint_improper_graphik_5.png)
If you did look at a graph first and did this the more efficient way, give yourself a pat on the back. Or a carrot.