evaluate integral of 1/x^2+x+1

[newtagi]

hi everyone, I need help to solve this problem. integral 1/x²+x+1

 

[Deleted member 4993]

hi everyone, I need help to solve this problem. integral 1/x²+x+1

Is it $\displaystyle \displaystyle{\dfrac{1}{x^2} \ + \ x \ + \ 1}$

or

$\displaystyle \displaystyle{\dfrac{1}{x^2 + x + 1}}$ ?

What are your thoughts?

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[Vect]

Use and memorize this formula: < link to objectionable page removed >

 

[SAMUELK]

Trig substitution?

hi everyone, I need help to solve this problem. integral 1/x²+x+1

Assuming you mean: 1/(x^2 + x + 1), how about completing the square?
x^2 + x + 1 = x^2 + x + 1/4 + 3/4
= (x + 1/2)^2 + 3/4
Now you should be able to do something with substitutions to get:
1/(u^2 + a^2)
and you're on your way.

 

[newtagi]

Sorry( ma fault. Actually it was (x+1)/(x^2+x+1) and I divided it into two fractions. They are (2x+1)/(x^2+x+1) and 1/(x^2+x+1). I solved first fraction, but I do not know what to do whith second fraction. I wrote something, can you check it?please. Is it right? I used as you said trig substitution .