Math Help - Integral - Show me the steps?

1. Integral - Show me the steps?

Hello,

The problem I'm working on is:

The integral of: (x^2 + 2)/(x+1)^2

Can you please step me through this problem?

Thanks!

2. Re: Integral - Show me the steps?

I would manipulate the integrand as follows:

$\frac{x^2+2}{(x+1)^2}=\frac{x^2+2x+1-2x+1}{(x+1)^2}=\frac{(x+1)^2-2x+1}{(x+1)^2}=1-\frac{2x-1}{(x+1)^2}=$

$1-\frac{2x+2-3}{(x+1)^2}=1-\frac{2(x+1)-3}{(x+1)^2}=1-\frac{2}{x+1}+\frac{3}{(x+1)^2}$

Now, integrate term by term.