Tìm \(\int {\dfrac{{5x + 1}}{{{x^2} - 6x + 9}}\,dx...

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- Hướng dẫn giải

Ta có: \(\int {\dfrac{{5x + 1}}{{{x^2} - 6x + 9}}\,dx} \)

\(= \int {\dfrac{{5\left( {x - 3} \right) + 16}}{{{{\left( {x - 3} \right)}^2}}}} \,dx \)

\(= \int {\left( {\dfrac{5}{{x - 3}} + \dfrac{{16}}{{{{\left( {x - 3} \right)}^2}}}} \right)} \,d\left( {x - 3} \right)\)

\( = 5\ln \left| {x - 3} \right| - \dfrac{{16}}{{\left( {x - 3} \right)}} + C\)