How can I solve a definite integral containing exponential function?

[zizou22]

I am trying to use integration by parts and evaluate .

So far I have gotten it to and
I applied:
But I didn't get a result. I will appreciate any hints. Thank you.

 

[tkhunny]

1) Why do you believe it can be done?
2) Why did you try Integration by Parts?
3) What is the genesis of this integral? What were you trying to do?

 

[Romsek]

I see 2F1 in there. That's a sure sign you've used software to go from g' to g.

If you're going to do that why not just use that software for the entire integral?