Integral of x/(x + 1)²(x+2)²

I suppose you mean the integral

Break up the integrand into partial fractions:

Solve for the coefficients:

So we have

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.