Definite integral

Question

What is the definite ∫((x²-3x+2)/(x+1)) ?

 

I tried dividing this but I didn't know what to do with the remainder. 

 

Answer 1

Divide synthetically or by using long division:

 

-1⌋ 1     -3     2

    _____-1___4

     1     -4     6

 

So, (x²-3x+2)/(x+1) = x-4 + 6/(x+1)

 

∫[(x²-3x+2)/(x+1)]dx = ∫[x-4+6/(x+1)]dx

 

                               = x²/2 - 4x + 6ln l x+1 l + C