intergrate 2x-14/4x^2-2x-3
4x^2 - 2x - 3 = 1/4 (16x^2-8x-12)
= 1/4 ((16x^2-8x+1) - 13)
= 1/4 ((4x-1)^2 - 13)
= 1/4 (4x-1+√13)(4x-1-√13)
if you let u = 4x-1, you have u^2-13 in the denominator, and almost du on top.
If you go to wolframalpha.com and type in
integral (2x-14)/(4x^2-2x-3) dx
you will see what some algebraic manipulation gets you.