Answer
$\dfrac{4}{3} \sinh (3x -\ln 2) +C$
Work Step by Step
Since, $\int \cosh x dx=\sinh x +C$
As we are given that $\int 4 \cosh ( 3x -\ln 2) dx$
Plug $3x -\ln 2 = a \implies 3 dx=da$
or, $dx=\dfrac{1}{3} da$
Thus,
$\int 4 \cosh ( 3x -\ln 2) dx=\dfrac{4}{3} \int (\cosh a) da= \dfrac{4}{3} (\sinh a) +C=\dfrac{4}{3} \sinh (3x -\ln 2) +C$
