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Find the antiderivative of f(x) = sin(ln(x)).
A. x/2 [sin(ln(x)) + cos(ln(x))] + C, for some constant C.
B. sin(ln(x)) - cos(ln(x)) + C, for some constant C.
C. sin(ln(x)) + cos(ln(x)) + C, for some constant C.
D. x/2 [sin(ln(x)) - cos(ln(x))] + C, for some constant C.

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