MCQ
$\int_{}^{} {\frac{{\cos 2x + x + 1}}{{{x^2} + \sin 2x + 2x}}} \;dx = $
- A$\log ({x^2} + \sin 2x + 2x) + c$
- B$ - \log ({x^2} + \sin 2x + 2x) + c$
- ✓$\frac{1}{2}\log ({x^2} + \sin 2x + 2x) + c$
- DNone of these
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$f(x)=e^{x-1}-e^{-|x-1|} \text { and } g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right) \text {. }$ Then the area of the region in the first quadrant bounded by the curves $y=f(x), y=g(x)$ and $x=0$ is