$\int\limits_{0}^{1}\frac{2x+5}{x^{2}-2x-5}dx$
Ta có:
$I=\int\limits_{0}^{1}\dfrac{2x+5}{x^2-2x-5}dx$
    $=\int\limits_{0}^{1}\dfrac{2x+5}{(x-1+\sqrt6)(x-1-\sqrt6)}dx$
    $=\dfrac{1}{12}\int\limits_{0}^{1}\dfrac{(12+7\sqrt6)(x-1+\sqrt6)+(12-7\sqrt6)(x-1-\sqrt6)}{(x-1+\sqrt6)(x-1-\sqrt6)}dx$
    $=\dfrac{1}{12}\int\limits_0^1\left(\dfrac{12-7\sqrt6}{x-1+\sqrt6}-\dfrac{12+7\sqrt6}{1+\sqrt6-x}\right)dx$
    $=\dfrac{1}{12}\left((12-7\sqrt6)\ln(x-1+\sqrt6)+(12+7\sqrt6)\ln(1+\sqrt6-x)\right)\left|\begin{array}{l}1\\0\end{array}\right.$
    $=\ln\dfrac{6}{5}-\dfrac{7}{2\sqrt6}\ln\dfrac{\sqrt6+1}{\sqrt6-1}$
sao từ 2x cộng 5 lại thành như vậy hả bạn –  ngolam39 13-07-13 04:21 PM

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