Answer
$\dfrac{4}{3} \sinh (3x -\ln 2) +C$
Work Step by Step
Given: $\int 4 \cosh ( 3x -\ln 2) dx$
Use the identity: $\int \cosh x dx=\sinh x +C$
Plug in $3x -\ln 2 = a \implies 3 dx=da$
or, $dx=\dfrac{1}{3} da$
Then:
$\int 4 \cosh ( 3x -\ln 2) dx=\dfrac{4}{3} \int \cosh a da= \dfrac{4}{3} \sinh a +C$
or, $=\dfrac{4}{3} \sinh (3x -\ln 2) +C$
