Integral of ((x/a)^x + (a/x)^x) times log x: find the antiderivative

1. A.
   $\left( \frac{x}{2} \right)^{x} + \left( \frac{2}{x} \right)^{x} + C$
2. B.
   $\left( \frac{x}{2} \right)^{x} - \left( \frac{2}{x} \right)^{x} + C$
3. C.
   $\left( \frac{x}{2} \right)^{x}\log_{2}\left( \frac{x}{2} \right) + C$
4. D.
   $\left( \frac{x}{2} \right)^{x}\log_{2}\left( \frac{2}{x} \right) + C$

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1. A.
   1
2. B.
   -4
3. C.
   -8
4. D.
   4

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