MCQ
$\int_1^e {\frac{{1 + \log x}}{x}\,dx = } $
- ✓$\frac{3}{2}$
- B$\frac{1}{2}$
- C$\frac{1}{e}$
- DNone of these
==> $[{\log _e}x]_1^e + \left[ {\frac{{{{(\log x)}^2}}}{2}} \right]_1^e = \frac{3}{2}$.
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$(A)$ $f(x)$ is monotonically increasing on $[1, \infty)$
$(B)$ $f(x)$ is monotonically decreasing on $(0,1)$
$(C)$ $f(x)+f\left(\frac{1}{x}\right)=0$, for all $x \in(0, \infty)$
$(D)$ $f\left(2^x\right)$ is an odd function of $x$ on $R$