Tricky Indefinite Integral

Question

$\int \frac{(x^2 + x)}{(e^x + x + 1)^2}dx$

I was thinking along the lines of breaking the numerator into denominator differentiation and generic function with help of division rule.

Answer 1

HINT:

Divide the numerator & denominator by $e^{2x}$

$$\dfrac{x^2+x}{(e^x+x+1)^2}=\dfrac{xe^{-x}\cdot(x+1)e^{-x}}{\{1+e^{-x}(x+1)\}^2}$$

Set $1+e^{-x}(x+1)=u$