$\int \cos \left(\log x\right)dx$ is equal to (A) $\frac{x}{2}\left(\cos \left(\log x\right)-\sin \left(\log x\right)\right)+c$ (B) $x\left(\cos \left(\log x\right)+\sin \left(\log x\right)\right)+c$ (C) $\frac{x}{2}(\cos \left(\log x\right)+\sin \left(\log x\right)+c$ (D) $x\left(\cos \left(\log x\right)-\sin \left(\log x\right)\right)+c$

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