Question

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

Answer 1

Hmm, maybe by parts.

Answer 2

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

Answer 3

Long division?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

got stuck on that part

Answer 9

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

Answer 10

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