Integrate 1/(x^2 - 2x + 4) using Homework Equations and a Step-by-Step Method

[Pyroadept]

Homework Statement

Integrate the following: ∫[1/(x^2 - 2x + 4)]dx

Homework Equations

∫[1/(x^2 + a^2)]dx = [1/a](arctan(x/a)) + C

The Attempt at a Solution

Let A = x^2 - 2x + 4 = x^2 - 2x + 1 + 3
= (x - 1)^2 + (√3)^2

So ∫[1/A]dx = [1/√3]arctan[(x-1)/√3] + C

Is this correct?

Thanks for any help

 

[gabbagabbahey]

Looks good to me