# Integral of an exponential function

1. Sep 12, 2010

### asi123

1. The problem statement, all variables and given/known data

Hey guys.

How do I solve this integral?

http://img816.imageshack.us/img816/208/68315659.png [Broken]

I've not been doing this for a long time :)

Thanks a lot.

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 4, 2017
2. Sep 12, 2010

### snipez90

Re: Integral

Show some work, and explain what tools you have to work with. Definite integrals can be computed in many ways.

3. Sep 12, 2010

### JetteroHeller

Re: Integral

You can use integration by parts. Using u = e^-t and dv = t^-2 dt

4. Sep 12, 2010

### asi123

Re: Integral

Yeah, but then I'll get some kind of Ln(t)*e^-t, no?

5. Sep 12, 2010

### snipez90

Re: Integral

Actually you may want to check convergence.

6. Sep 12, 2010

### JetteroHeller

Re: Integral

I was actually thinking:
you perform integration by parts once to reduce t^2 to t.
Result is that one of the terms is integral((e^-t)/t)
Rewrite that term to become integral(1/te^t)

use the following identity from integral tables: integral(ue^u) = (u-1)e^u
the rest is taking limits.