Integrating a Tricky Fraction: Solving ∫(1/(x^2-x+1)dx

[hms.tech]

Homework Statement

∫(1/(x^2-x+1)dx

Homework Equations

No idea

The Attempt at a Solution

I tried this by the subsitution method but that attempt was feeble as it only complicated the integral even further.
let t=x^2-x+1

this integral can neither be split into partial fractions.

I have no idea how to proceed forward.

 

[phyzguy]

Write (x^2 - x +1) as (x-1/2)^2 +3/4. Then make the substitution u=x-1/2. Now the integrand is in the form of 1/(u^2 + a^2), which hopefully you know how to do with a trigonometric substitution.