MCQ
The integral $\int \limits_{1}^{2} e ^{ x } \cdot x ^{ x }\left(2+\log _{ e } x \right) d x$ equal
- A$e (4 e +1)$
- B$e(2 e-1)$
- C$4 e^{2}-1$
- ✓$e (4 e -1)$
$\int_{1}^{2} e ^{ x }\left(2 x ^{ x }+ x ^{ x } \log _{ e } x \right) d x$
$\int_{1}^{2} e ^{ x }(\frac{ x ^{ x }}{f( x )}+\underbrace{ x ^{ x }\left(1+\log _{ e } x \right)}_{f^{(}( x )}) d x$
$\left( e ^{ x } \cdot x ^{ x }\right)_{1}^{2}=4 e ^{2}- e$
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($A$) $\mathrm{M}$ is invertible
($B$) There exists a nonzero column matrix $\left(\begin{array}{l}a_1 \\ a_2 \\ a_3\end{array}\right)$ such that $M\left(\begin{array}{l}a_1 \\ a_2 \\ a_3\end{array}\right)=\left(\begin{array}{l}-a_1 \\ -a_2 \\ -a_3\end{array}\right)$
($C$) The set $\left\{\mathrm{X} \in \mathbb{R}^3: \mathrm{MX}=\mathbf{0} \neq \neq 0\right\}$, where $\mathbf{0}=\left(\begin{array}{l}0 \\ 0 \\ 0\end{array}\right)$
($D$) The matrix $(M-2 I)$ is invertible, where $I$ is the $3 \times 3$ identity matrix