Câu hỏi 22

Đặt \(\left\{ \begin{array}{l}u = \ln x\\dx = {x^2}dx\end{array} \right.\)\( \Rightarrow \left\{ \begin{array}{l}du = \dfrac{1}{x}dx\\v = \dfrac{{{x^3}}}{3}\end{array} \right.\)

\( \Rightarrow I = \left. {\left( {\dfrac{{{x^3}}}{3}\ln x} \right)} \right|_1^e - \int\limits_1^e {\left( {\dfrac{{{x^3}}}{3}.\dfrac{1}{x}} \right)dx}  = \dfrac{{{e^3}}}{3} - \dfrac{1}{3}\int\limits_1^e {{x^2}dx}  = \dfrac{{{e^3}}}{3} - \left. {\dfrac{1}{3}.\dfrac{{{x^3}}}{3}} \right|_1^e = \dfrac{{{e^3}}}{3} - \dfrac{{{e^3}}}{9} + \dfrac{1}{9} = \dfrac{2}{9}{e^3} + \dfrac{1}{9}\) 

\( \Rightarrow a = \dfrac{2}{9},b = \dfrac{1}{9} \Rightarrow 9\left( {a + b} \right) = 3\).

Chọn A.