Answer
$-(\dfrac{2x+1}{2})\cos (2x-1) +\dfrac{1}{2} \sin (2x-1) +C $
Work Step by Step
Our aim is to solve the integral $ \int (2x+1) \sin (2x-1) \ dx$
Use integration by parts formula.
$ \int (2x+1) \sin (2x-1) \ dx=(-\dfrac{2x+1}{2})\times \cos (2x-1) +\int \cos (2x-1) \ dx $
or, $=-(\dfrac{2x+1}{2})\cos (2x-1) +\dfrac{1}{2} \sin (2x-1) +C $
