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\(\text{ The integral }\int \left({\left(\frac{x}{2}\right)}^{x}+{\left(\frac{2}{x}\right)}^{x}\right)\log \left(\frac{e…

Q1

\(\text{ The integral }\int \left({\left(\frac{x}{2}\right)}^{x}+{\left(\frac{2}{x}\right)}^{x}\right)\log \left(\frac{ex}{2}\right)dx\text{ is equal to }\)

[JEE Main 2023, 08 Apr (Shift 2)]

a

\({\left(\frac{x}{2}\right)}^{x}+{\left(\frac{2}{x}\right)}^{x}+C\)

b

\({\left(\frac{x}{2}\right)}^{x}-{\left(\frac{2}{x}\right)}^{x}+C\)

c

\({\left(\frac{x}{2}\right)}^{x}{\log }_{2}\left(\frac{x}{2}\right)+C\)

d

\({\left(\frac{x}{2}\right)}^{x}{\log }_{2}\left(\frac{2}{x}\right)+C\)

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