Set up partial fractions for x(x+1)2\dfrac{x}{(x+1)^2}(x+1)2x.
Ax+1+B(x+1)2\dfrac{A}{x+1} + \dfrac{B}{(x+1)^2}x+1A+(x+1)2B
Ax+B(x+1)2\dfrac{Ax+B}{(x+1)^2}(x+1)2Ax+B
A(x+1)2\dfrac{A}{(x+1)^2}(x+1)2A
Ax+Bx+1\dfrac{A}{x} + \dfrac{B}{x+1}xA+x+1B