Integrals of sin(log x) and cos(log x) by parts twice

1. A.
   $\frac{x}{2}(\sin(\log x)-\cos(\log x))+c$
2. B.
   $x(\cos(\log x)-\sin(\log x))+c$
3. C.
   $\frac{x}{2}(\cos(\log x)+\sin(\log x))+c$
4. D.
   $x(\cos(\log x)+\sin(\log x))+c$

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1. A.
   $-\frac{x}{2}(\sin(\log x)-\cos(\log x))+c$
2. B.
   $\frac{x}{2}(\sin(\log x)-\cos(\log x))+c$
3. C.
   $\frac{x}{2}(\sin(\log x)+\cos(\log x))+c$
4. D.
   $-\frac{x}{2}(\sin(\log x)+\cos(\log x))+c$

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1. A.
   $\dfrac{x}{2}[\sin(\log x) - \cos(\log x)] + c$
2. B.
   $\dfrac{x}{2}[\sin(\log x) + \cos(\log x)] + c$
3. C.
   $\dfrac{x}{2}[\cos(\log x) - \sin(\log x)] + c$
4. D.
   $\dfrac{x}{4}[\cos(\log x) - \sin(\log x)] + c$

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1. A.
   $\sin(\log x)$
2. B.
   $-\cos(\log x)$
3. C.
   $-\sin(\log x)$
4. D.
   $\cos(\log x)$

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