Biết rằng $\Large I=\int\limits_{2}^{3}{x\ln xdx=m\ln 3+n\ln 2+p}$ , t

Biết rằng $\Large I=\int\limits_{2}^{3}{x\ln xdx=m\ln 3+n\ln 2+p}$ , trong đó $\Large m,n,p\in \mathbb{Q}$ . Tính $\Large m+n+2p$

• A.

  $\Large \dfrac{5}{4}$

• B.

  $\Large \dfrac{9}{2}$

• C.

  $\Large 0$

• D.

  $\Large -\dfrac{5}{4}$

Đặt $\Large \left\{ \begin{align}  & u=\ln x \\  & dv=xdx \\ \end{align} \right.$ $\Large \Rightarrow \left\{ \begin{align}  & du=\dfrac{1}{x}dx \\  & v=\dfrac{{{x}^{2}}}{2} \\ \end{align} \right.$ 

Suy ra $\Large I=\dfrac{{{x}^{2}}}{2}\ln x\left| \begin{align}  & 3 \\  & 2 \\ \end{align} \right.$ $\Large -\dfrac{1}{2}\int\limits_{2}^{3}{xdx=\dfrac{9}{2}}\ln 3-2\ln 2-\dfrac{5}{4}$

Suy ra: $\Large m= \dfrac{9}{2}; n= -2; p= -\dfrac{5}{4}$

Suy ra $\Large m+n+2p=0$

Chọn đáp án C