Cho . Giá trị a + b là:

* Hướng dẫn giải

\(I = \int\limits_0^1 {\frac{1}{{3 + 2x - {x^2}}}} dx \\= \int\limits_0^1 {\left( {\frac{{\frac{1}{4}}}{{x + 1}} + \frac{{\frac{1}{4}}}{{3 - x}}} \right)} \\= \frac{1}{4}\left. {\left( {\ln \left| {x + 1} \right| - \ln \left| {x - 3} \right|} \right)} \right|_0^1 \\= \frac{1}{4}\ln 3 \Rightarrow a = b = \frac{1}{4} \\\Rightarrow a + b = \frac{1}{2}\)