Answer
$2 \sin (2x-1)++C$
Work Step by Step
Our aim is to solve the integral $ \int 4 \cos (2x-1)\ dx$
Let us consider that $a =2x-1$ and $dx=\dfrac{da}{2}$
Now, $\int 4 \cos (2x-1) \ dx = \int 4 \cos a \times (\dfrac{1}{2}) (da)$
or, $=2 \int \cos a da $
or, $=2 \sin (2x-1)++C$
