Tích phân \int\limits_0^2 {\frac{x}{{{x^2} + 3}}{\rm{d}}x} bằng

* Hướng dẫn giải

\(\int\limits_0^2 {\frac{x}{{{x^2} + 3}}{\rm{d}}x}  = \frac{1}{2}\int\limits_0^2 {\frac{1}{{{x^2} + 3}}\,{\rm{d}}\left( {{x^2} + 3} \right)}  = \left. {\frac{1}{2}\ln \left| {{x^2} + 3} \right|} \right|_0^2 = \frac{1}{2}\ln \frac{7}{3}\)