What is the integral of 2cos(2x)+1 ?

The integral of 2cos(2x)+1 is sin(2x)+x+C

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integral of 2cos(2x)+1

\int 2 cos (2 x) + 1 d x

sin (2 x) + x + C

Solution steps

\int 2 cos (2 x) + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 cos (2 x) d x + \int 1 d x

\int 2 cos (2 x) d x = sin (2 x)

\int 1 d x = x

= sin (2 x) + x

Add a constant to the solution

= sin (2 x) + x + C