What is the integral of 4sin(x)+8 ?

The integral of 4sin(x)+8 is -4cos(x)+8x+C

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integral of 4sin(x)+8

integral

4 sin (x) + 8

- 4 cos (x) + 8 x + C

Solution steps

\int 4 sin (x) + 8 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 4 sin (x) d x + \int 8 d x

\int 4 sin (x) d x = - 4 cos (x)

\int 8 d x = 8 x

= - 4 cos (x) + 8 x

Add a constant to the solution

= - 4 cos (x) + 8 x + C

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