Divide $\displaystyle x+ 1 $ into $\displaystyle x^2 3x 5 $ obtaining the quotient $\displaystyle x 4 $ and the remainder $\displaystyle 1 $.
So $\displaystyle \frac {x^2 3x  5} {x + 1} = (x+1)(x4) + \frac {1}{x+1} $
Then Integrate the polynomial and the fraction separately.
