Đáp án:

• Đặt \( t = x + 1 \Rightarrow x = t - 1 \Rightarrow dx = dt \)  

• \( \int \frac{x^2}{(x + 1)^{10}} \, dx = \int \frac{(t - 1)^2}{t^{10}} \, dt \)

\( = \int \left( \frac{1}{t^8} - \frac{2}{t^9} + \frac{1}{t^{10}} \right) \, dt = -\frac{8}{t^7} + \frac{18}{t^8} - \frac{10}{t^9} + C \)

\( = -\frac{8}{(x + 1)^7} + \frac{18}{(x + 1)^8} - \frac{10}{(x + 1)^9} + C \)