integration - Help me Evaluate this Integral

I have this problem $\int \frac {-5x + 11}{{(x+1)(x^2+1)}} \text{d}x$

And i'm not sure how to deal with this. I've tried substitution and getting nowhere. I've peeked at the answer and there a trigonometric part with arctan. Do i use Partial fraction expansion here?

Thanks

Answer

use the partial fraction to get
$$\frac{-5x+11}{(x+1)(x^2+1)}=\frac{3-8x}{x^2+1}+\frac{8}{x+1}=\frac{3}{x^2+1}-\frac{8x}{x^2+1}+\frac{8}{x+1}$$

details:

$$\frac{-5x+11}{(x+1)(x^2+1)}=\frac{Ax+B}{x^2+1}+\frac{C}{1+x}=\frac{(Ax+B)(1+x)+C(x^2+1)}{(x^2+1)(1+x)}$$
$$\frac{-5x+11}{(x+1)(x^2+1)}=\frac{Ax+Ax^2+B+Bx+Cx^2+C}{(x^2+1)(1+x)}$$
$$A+B=-5$$

$$A+C=0$$
$$B+C=11$$

solve these simultaneous equations to get
$A=-8$
$B=3$

$C=8$
so the integral will be
$$\int (\frac{3}{x^2+1}-\frac{8x}{x^2+1}+\frac{8}{x+1})dx=3\tan^{-1}x-4\log(x^2+1)+8\log(x+1)+C$$