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Câu hỏi: Nguyên hàm $\int{\dfrac{1}{{{x}^{2}}-7x+6}dx}$ là:
A. $\dfrac{1}{5}\ln \left| \dfrac{x-1}{x-6} \right|+C$.
B. $\dfrac{1}{5}\ln \left| \dfrac{x-6}{x-1} \right|+C$.
C. $\dfrac{1}{5}\ln \left| {{x}^{2}}-7x+6 \right|+C$.
D. $-\dfrac{1}{5}\ln \left| {{x}^{2}}-7x+6 \right|+C$.
A. $\dfrac{1}{5}\ln \left| \dfrac{x-1}{x-6} \right|+C$.
B. $\dfrac{1}{5}\ln \left| \dfrac{x-6}{x-1} \right|+C$.
C. $\dfrac{1}{5}\ln \left| {{x}^{2}}-7x+6 \right|+C$.
D. $-\dfrac{1}{5}\ln \left| {{x}^{2}}-7x+6 \right|+C$.
Ta có:
$\int{\dfrac{1}{{{x}^{2}}-7x+6}dx}=\int{\dfrac{1}{\left( x-1 \right)\left( x-6 \right)}dx}=\dfrac{1}{5}\int{\left( \dfrac{1}{x-6}-\dfrac{1}{x-1} \right)dx}
=\dfrac{1}{5}\left( \ln \left| x-6 \right|-\ln \left| x-1 \right| \right)+C=\dfrac{1}{5}\ln \left| \dfrac{x-6}{x-1} \right|+C$.
$\int{\dfrac{1}{{{x}^{2}}-7x+6}dx}=\int{\dfrac{1}{\left( x-1 \right)\left( x-6 \right)}dx}=\dfrac{1}{5}\int{\left( \dfrac{1}{x-6}-\dfrac{1}{x-1} \right)dx}
=\dfrac{1}{5}\left( \ln \left| x-6 \right|-\ln \left| x-1 \right| \right)+C=\dfrac{1}{5}\ln \left| \dfrac{x-6}{x-1} \right|+C$.
Đáp án B.