Can You Tackle This Improper Integral Challenge?

[transgalactic]

i added a link with my question and how i tried to solve it
int the link

http://img141.imageshack.us/my.php?image=img8212eq4.jpg

 

[HallsofIvy]

Your limit is wrong. xln x- x goes to 0 as x goes to 0, not infinity. Rewrite it as xlnx- x= x(ln x- 1)= (ln x-1)/(1/x) and use L'Hopital's rule.

 

[transgalactic]

thanks