Tìm nguyên hàm của hàm số sau: ∫x2+1/(x−1)2(x+3)dx

Question

\(\int \frac{x^{2} +1}{\left(x-1\right)^{2} \left(x+3\right)} {\rm d}x \)

Answer 1

\( \begin{array}{l} {\int \frac{x^{2} +1}{\left(x-1\right)^{2} \left(x+3\right)} {\rm d}x =\int \left(\frac{3}{8} \cdot \frac{1}{x-1} +\frac{1}{2} \cdot \frac{1}{\left(x-1\right)^{2} } +\frac{5}{8} \cdot \frac{1}{x+3} \right){\rm d}x } \\ {\qquad =\frac{3}{8} \ln \left|x-1\right|-\frac{1}{2\left(x-1\right)} +\frac{5}{8} \ln \left|x+3\right|+C} \end{array}\)