Tính nguyên hàm \(\int - 7x + 7}}{{x - 2}}\,dx} \) ta

* Hướng dẫn giải

Ta có: \(\int {\dfrac{{2{x^2} - 7x + 7}}{{x - 2}}\,dx} \)

\(= \int {\dfrac{{2\left( {{x^2} - 4x + 4} \right) + x - 2 + 1}}{{x - 2}}} \,dx \)

\(= \int {\left( {2\left( {x - 2} \right) + 1 + \dfrac{1}{{x - 2}}} \right)} \,dx\)

\( = \left( {{x^2} - 3x + \ln \left| {x - 2} \right|} \right) + C\)