Can anyone tell me if the answer to this is: converges to -1/2

That depends. What are the limits? -infinity to 0? If so, then yes, it's -1/2.

What if it is from 2 to + inphinity??

In that event, no, it's not -1/2. Show me some of your workings and I'll be glad to point you in the right direction. BTW, I like your spelling of 'infinity'. That's the way it should be spelled.:) :)

Is this it?:

Haha wow I didn't even notice I wrote "infinity" that way. I'm so use to writing "inphinity" because "Inphinity" he is a great Euro Dj.

yes the problem does look like that. I think I realized where I went wrong. I someplace lost the squared (1+ x^2) ^2 . Therefore this time I get the answer to be - 1/10

Here is the new work:


Attachment 4203

I used u-sub to get the general integral of the problem and that I got -1/ 2(1+ x^2) dx that is where I got the third line numbers from. U = 1+ x^2 du= 2x dx 1/2 du = x dx

If I'm wrong anywhere where did I go wrong and why?

You did good. That's correct.