Đáp án:

• \( \int x .\frac{x^2}{x^4 + 3x^2 + 2} \, dx = \int u f(u) \, du \, \text{ với } u = x^2 \)

• Đặt \( t = x^2 \implies dt = 2x \, dx \)

• \( \int \frac{x^3}{x^4 + 3x^2 + 2} \, dx = \frac{1}{2} \int \frac{t}{(t + 1)(t + 2)} \, dt \)

• \(
\left(\frac{t}{(t + 1)(t + 2)} = \frac{A}{t + 1} + \frac{B}{t + 2} \implies  
\begin{cases} 
A = -1 \\ 
B = 2 
\end{cases}\right)
\)

\( = \frac{1}{2} \int \left( -\frac{1}{t + 1} + \frac{2}{t + 2} \right) dt = \ln|t + 2| - \frac{1}{2} \ln|t + 1| + C \)

\( = \ln(x^2 + 2) - \frac{1}{2} \ln(x^2 + 1) + C \)