What is the integral of 1/3 sin(3x)+2 ?

The integral of 1/3 sin(3x)+2 is -1/9 cos(3x)+2x+C

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integral of 1/3 sin(3x)+2

\int \frac{1}{3} sin (3 x) + 2 d x

- \frac{1}{9} cos (3 x) + 2 x + C

Solution steps

\int \frac{1}{3} sin (3 x) + 2 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 \frac{1}{3} sin (3 x) d x + \int 2 d x

\int \frac{1}{3} sin (3 x) d x = - \frac{1}{9} cos (3 x)

\int 2 d x = 2 x

= - \frac{1}{9} cos (3 x) + 2 x

Add a constant to the solution

= - \frac{1}{9} cos (3 x) + 2 x + C

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What is the integral of 1/3 sin(3x)+2 ?
The integral of 1/3 sin(3x)+2 is -1/9 cos(3x)+2x+C