hey can anyone tell me how to integrate (t+ 2t^2)/(t^2+t+1)

Question

anonymous · Answer

Hmm, maybe by parts.

anonymous · Answer

$u=t^2+t+1$ looks really tempting but it won't work.

psymon · Answer

Long division?

anonymous · Answer

got the solution 
2- (t+2)/ t^2+t+1 
t+2= p(2t+1)+q
split and integrate

psymon · Answer

Glad you saw how to integrate it from there, not bad, lol.

anonymous · Answer

its still a sub part of a question... :D

psymon · Answer

Oh, so you didnt solve it all the way? xD

anonymous · Answer

got stuck on that part

psymon · Answer

Im not sure what kind of substitution could work. If u were t^2 + t  +1, then du would be 2t+1. Only thing I can think of is find a way to manipulate -t-2 into looking like 2t+1 so itll cancel out when you let u = t^2 + t + 1

anonymous · Answer

you got that right, after integration there will be term of tan and log