What is the integral of 2cos(2x)-6 ?

The integral of 2cos(2x)-6 is sin(2x)-6x+C

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integral of 2cos(2x)-6

\int 2 cos (2 x) - 6 d x

sin (2 x) - 6 x + C

Solution steps

\int 2 cos (2 x) - 6 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 6 d x

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

\int 6 d x = 6 x

= sin (2 x) - 6 x

Add a constant to the solution

= sin (2 x) - 6 x + C