Cho \(\int {\frac{1}{{\sqrt {mx + {m^2} - 8} }}} dx = \frac{2}{3}\sqrt {3x + 1} + C\).

A. \( - \frac{1}{2}\left( {{e^\pi } + 1} \right)\)

B. \(\frac{1}{2}\left( {{e^\pi } + 1} \right)\)

C. \(\frac{1}{4}\left( {{e^\pi } - 1} \right)\)

D. \( - \frac{1}{4}\left( {{e^\pi } - 1} \right)\)