Đặt \(\left\{{}\begin{matrix}u=lnx\\dv=\dfrac{1}{x^2}dx\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}du=\dfrac{dx}{x}\\v=-\dfrac{1}{x}\end{matrix}\right.\)
\(I=-\dfrac{lnx}{x}|^a_1+\int\limits^a_1\dfrac{dx}{x^2}=-\dfrac{lna}{a}-\dfrac{1}{x}|^a_1=-\dfrac{lna}{a}-\dfrac{1}{a}+1\)
\(\Rightarrow\left\{{}\begin{matrix}1-\dfrac{1}{a}=\dfrac{1}{2}\\\dfrac{lna}{a}=\dfrac{ln2}{2}\end{matrix}\right.\) \(\Rightarrow a=2\)
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