Let \( A=\left[\begin{array}{ccc}x^{2} & 6 & 0 \\ 1 & -5 & 1 \\ 2 & 0 & x\end{array}\right] \) a...

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Let \( A=\left[\begin{array}{ccc}x^{2} & 6 & 0 \\ 1 & -5 & 1 \\ 2 & 0 & x\end{array}\right] \) and \( B=\left[\begin{array}{ccc}4 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 8\end{array}\right] \). If a function is defined as \( f(x)=\operatorname{trace}(A B) \), then \( \int \frac{3 d x}{f(x)} \) is equal to:
(a) \( \frac{1}{4} \ln \left|\frac{2 x-1}{2 x+5}\right|+c \)
(b) \( \frac{1}{4} \ln \left|\frac{2 x+5}{2 x-1}\right|+c \)
(c) \( \frac{1}{3} \ln \left|\frac{1-2 x}{2 x+5}\right|+c \)
(d) \( \frac{1}{3} \ln \left|\frac{1-2 x}{2 x+3}\right|+c \)
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