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
Like so:
$\displaystyle \int\frac{x-1}{(x-2)^{2}+1}$
Now, let $\displaystyle u=x-2, \;\ du=dx, \;\ u+1=x-1$
$\displaystyle \int\frac{u+1}{u^{2}+1}du=\int\frac{u}{u^{2}+1}+\i nt\frac{1}{u^{2}+1}du$
Now, make the observation that there will be an ln and arctan in your future.