## JoãoVitorMC 3 years ago Solve the following improper improper integral:

1. JoãoVitorMC

$\int\limits_{0}^{\infty} \frac{ \ln x }{ x² + a² }$

2. JoãoVitorMC

a > 0

3. kiki41554

Huh

4. mahmit2012

|dw:1350750759562:dw|

5. kiki41554

So it's -36

6. mahmit2012

|dw:1350750883133:dw|

7. kiki41554

Hello???

8. mahmit2012

|dw:1350751308660:dw|

9. mahmit2012

|dw:1350751339539:dw|

10. mahmit2012

Did you get it?

11. JoãoVitorMC

yeahh thank you so much!!

12. mahmit2012

Do you know what is a residual.

13. mahmit2012

|dw:1350751491113:dw|

14. mahmit2012

|dw:1350751564402:dw|

15. mahmit2012

because x=ai is an order one pole.

16. mahmit2012

this way is so easy, but your teacher will get confuse. Draw a contour and give my solution.

17. JoãoVitorMC

ok thank you!!

18. JoãoVitorMC

one question, i didn't understand this last part:

19. JoãoVitorMC

|dw:1350834795661:dw|

20. JoãoVitorMC

but you you did this:

21. JoãoVitorMC

|dw:1350834921089:dw| there is a 2 dividing see?