[TEX]\begin{array}{l}I = \int {\frac{{dx}}{{5x^2 - 8x + 6}}} = \frac{1}{5}.\int {\frac{{dx}}{{\left( {x - \frac{4}{5}} \right)^2 + \frac{{14}}{{25}}}}}\\Coi:x - \frac{4}{5} = \frac{{\sqrt {14} }}{5}\tan t \Rightarrow dx = \frac{{\sqrt {14} }}{5}.\frac{{dt}}{{c{\rm{os}}^2 t}}\\\left( {x - \frac{4}{5}} \right)^2 + \frac{{14}}{{25}} = \frac{{14}}{{25}}\left({\tan ^2 t + 1} \right) \Rightarrow \frac{{dx}}{{\left( {x - \frac{4}{5}} \right)^2 + \frac{{14}}{{25}}}} = \frac{{\sqrt {14} }}{5}.\frac{{dt}}{{c{\rm{os}}^2 t}}.\frac{1}{{\frac{{14}}{{25}}\left( {\tan ^2 t + 1} \right)}}\\= \frac{5}{{\sqrt {14} }} \Rightarrow I = \frac{1}{5}.\frac{5}{{\sqrt {14} }}\int {dt = } \frac{1}{{\sqrt {14} }}t + C = \frac{1}{{\sqrt {14} }}{\rm{arctan}}\left( {\frac{{5x - 4}}{{\sqrt {14} }}} \right) + C \\\\\end{array}[/TEX]
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