What is the integral of 5cos(5x)-4 ?

The integral of 5cos(5x)-4 is sin(5x)-4x+C

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integral of 5cos(5x)-4

\int 5 cos (5 x) - 4 d x

sin (5 x) - 4 x + C

Solution steps

\int 5 cos (5 x) - 4 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 5 cos (5 x) d x - \int 4 d x

\int 5 cos (5 x) d x = sin (5 x)

\int 4 d x = 4 x

= sin (5 x) - 4 x

Add a constant to the solution

= sin (5 x) - 4 x + C