Integral using partial fraction

[Lord Dark]

Homework Statement

integral using partial fraction

Hi everyone ,,

got the following question :

Integrate using partial fraction :

integral ( (4x^2+3)/(x^2+x+1)^2 )

The attempt at a solution

I reached the following ,,

integral ( 4/(X^2+x+1) + (-4x-1)/(X^2+x+1)^2) )

and now I don't know how to integrate .. -_-

help please

 

[sutupidmath]

here is a hint:

x^2+x+1=(x+1/2)^2+3/4, use subst: (sqrt(3)/2)*t=x+1/2, do you see why?

the second one: for the numerator: -(4x+1)=-(4x+2-1)=-2(2x+1)+1 then separate the fractions, for the first fraction use subst. u=x^2+x+1, do u see why? for the second fracction, proceed using the first hint i gave initially.

come back if you have more questions.

 

[Lord Dark]

thx m8 ,, I'll check the hints ,, and I'll come back If i have more questions :)

 

[Lord Dark]

thanks very much sutupidmath ,, I've answered it thanks to your hint ,, thanks again :)