integrate (x+x^2)^2 over x^3?

Question

also what is the intgral of 1/x(1+1/x)^3

Answer 1

(x + x^2)^2 / x^3 =
(x^2 + 2x^3 + x^4) / x^3 =
(1/x) + 2 + x

This is easy enough to integrate by integrating each term and adding up the results:
Ln(x) + 2x + (x^2)/2 + c

Answer 2

I = ∫ (x^(4) + 2.x³ + x²) / x³ dx
I = ∫ (x + 2 + 1 / x ) dx
I = x ² / 2 + 2x + log x + C

Answer 3

(x^2+x^4+2x^3)/x^3
1/x+x+2
if we integrate this we get
logx+(x^2)/2+2x+c