Tìm nguyên hàm \(\int\limits_{{}}^{{}}{\frac{1}{x\left( x-3 \right)}dx}\)
Giải chi tiết:
Ta có: \(\frac{1}{x\left( x-3 \right)}=\frac{1}{3}.\left( \frac{1}{x-3}-\frac{1}{x} \right)\)
\(\Rightarrow \int\limits_{{}}^{{}}{\frac{1}{x\left( x-3 \right)}dx}=\frac{1}{3}\int\limits_{{}}^{{}}{\left( \frac{1}{x-3}-\frac{1}{x} \right)dx}=\frac{1}{3}\ln \left| \frac{x-3}{x} \right|+C\)
Chọn D.