Question

what is the integration of 4x^2-2x+2/4x^2-4x+3

Answer 1

\[\int\limits (4x^2-2x+2/4x^2-4x+3) dx\]

Answer 2

first step would be use long division

Answer 3

\[\rightarrow \int\limits_{}^{}1 + \frac{2x-1}{4x^{2}-4x+3} dx\]
then make substitution
u = 4x^2 -4x +3
du = 8x-4 = 4(2x-1) dx
\[\rightarrow x +\frac{1}{4}\int\limits_{}^{}\frac{1}{u} du\]

Answer 4

thanks how did you do long division?

Answer 5

1 + (2x-1)/(4x^2-4x+3)
___________________
4x^2 -4x +3 | 4x^2 -2x +2
-(4x^2 -4x +3)
--------------
2x -1

Answer 6

oh k thats how it works