Thread: Quick Integration problem

This is not a very difficult problem, it's just that I did calc 2 a while back and I'm really rusty. Here goes:

Int(1/(1+x+x^2))dx

The problem I'm having is not with the integration per say, but everything leading up to it. I'm pretty sure you have to manipulate it so that it is in the form 1/(1+u^2) and then use arctan, but I can't seem to do that. So whoever decides to answer this question, can you please show all the steps. Thanks

Originally Posted by Jhevon

This is not a very difficult problem, it's just that I did calc 2 a while back and I'm really rusty. Here goes:

Int(1/(1+x+x^2))dx

The problem I'm having is not with the integration per say, but everything leading up to it. I'm pretty sure you have to manipulate it so that it is in the form 1/(1+u^2) and then use arctan, but I can't seem to do that. So whoever decides to answer this question, can you please show all the steps. Thanks

You are correct.
You need to use a classic trick, "completing the square".

Thanks a lot, got it.

This integral produces an inverse trig. function



Applyin' this, yields: