Tìm: a) nguyên hàm (2x - 1) / x+ 1; b) nguyên hàm (3 + 2 sim^2(x))

a) \(\int {\frac{{2x - 1}}{{x + 1}}dx} \) = \(\int {\left[ {\frac{{2\left( {x + 1} \right) - 3}}{{x + 1}}} \right]dx} \)

                      = \(\int {2dx - \int {\frac{3}{{x + 1}}dx} } \)

                      = 2x – 3ln\(\left| {x + 1} \right|\) + C.

b) \(\int {\left( {3 + 2{{\sin }^2}x} \right)dx} \) = \(\int {\left( {3 + 2.\frac{{1 - \cos 2x}}{2}dx} \right)} \)

                                 = \(\int {\left( {3 + 1 - \cos 2x} \right)dx} \)

                                 = \(\int {\left( {4 - \cos 2x} \right)dx} \)

                                 = 4x − \(\int {\cos 2x.\frac{{{{\left( {2x} \right)}^\prime }}}{2}dx} \)

                                 = 4x − \(\frac{{\sin 2x}}{2}\) + C.