integration help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

∫(x^2+2x)dx/(x+1)^2

Answer 1

∫(x^2+2x)dx/(x+1)^2

= ∫(x^2 + 2x + 1 - 1)dx/(x+1)^2

= ∫((x + 1)^2 - 1)dx/(x+1)^2

= ∫((x + 1)^2) / ((x + 1)^2)dx - ∫dx/(x+1)^2

Cancel common terms.

= ∫dx - ∫dx(x+1)^(-2)

Formula : ∫x^n = (x^(n+1))/(n+1)

= x - {(x+1)^(-2+1)} / (-2+1)

= x - {(x+1)^(-1)} / (-1)

= x + {(x+1)^(-1)}

= x + {1/(x+1)}