I need help finishing integration, from 1 to 2, of (x^2-2x+3)/(x^2-x+2)

[Lexy234]

The integral from 1 to 2 (x^2-2x+3)/(x^2-x+2)
First I did long division, then after a usub and integrating I came up with 1/2x-lnu evaluated at 1 to 2... I'm sorry if this is confusing, I attached a picture. I'm just confused on what to do next..should I change the limits to terms of U, should I put U back in terms of the original equation then evaluate? Thank you!

 

[tkhunny]

Looks like you are so troubled that you don't know which way is up.

Why is du = stuff/2? I'm puzzled by the division by 2.

Why is the first antiderivative term x/2. Again I'm puzzled by the division by 2.

If the lower degree numerator is not EXACTY the first derivative of the denominator, you may have a trigonometric substitution in your future.

Note: \(\displaystyle \dfrac{2x-1}{2}\ne x-1\) -- Try that again. This goes to my just previous point. You wanted so badly the numerator to be exactly the first derivative of the denominator, that you made it happen - forgetting your algebra in the process.