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!
I would manipulate the integrand as follows:
$\displaystyle \frac{x^2+2}{(x+1)^2}=\frac{x^2+2x+1-2x+1}{(x+1)^2}=\frac{(x+1)^2-2x+1}{(x+1)^2}=1-\frac{2x-1}{(x+1)^2}=$
$\displaystyle 1-\frac{2x+2-3}{(x+1)^2}=1-\frac{2(x+1)-3}{(x+1)^2}=1-\frac{2}{x+1}+\frac{3}{(x+1)^2}$
Now, integrate term by term.