# Math Help - Integration via completing the square

1. ## Integration via completing the square

When using completing the squares on a fraction do I alter both the numerator and denominator? ex... (x-1)/(x^2-4x+5) ???/(x-2)^2+1

2. Like so:

$\int\frac{x-1}{(x-2)^{2}+1}$

Now, let $u=x-2, \;\ du=dx, \;\ u+1=x-1$

$\int\frac{u+1}{u^{2}+1}du=\int\frac{u}{u^{2}+1}+\i nt\frac{1}{u^{2}+1}du$

Now, make the observation that there will be an ln and arctan in your future.