Answer
$12 \sinh (\dfrac{x}{2} -\ln 3 )+ C$
Work Step by Step
Since, we have $\int \cosh x dx=\sinh x +C$
Then,plug $\dfrac{x}{2} -\ln 3 = a \implies \dfrac{dx}{2}=da$
or, $dx=2 da$
Thus, $\int 6 \cosh (\dfrac{x}{2} -\ln 3) dx=\int 6 (\cosh a) (2 da)= 12 \sinh a +C$
or, $=12 \sinh (\dfrac{x}{2} -\ln 3 )+ C$
