how would i integrate
$\displaystyle \int \frac{dx}{4x^{2}-4x +17} $
When dealing with a reciprocal quadratic you either need to complete the square or factorise.
In this case you need to complete the square.
you should get $\displaystyle \int \frac{dx}{(2x-1)^2 +4^2} $
now use the substitution $\displaystyle 2x-1 = 2 \tan u$
give this a shot on your own and see how it goes.
For checking purposes only, the answer is $\displaystyle \frac{1}{8} \arctan \left( \frac{2x - 1 }{4} \right)$.
Bobak