What is the integral of 1+cos(3x) ?

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

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integral of 1+cos(3x)

\int 1 + cos (3 x) d x

x + \frac{1}{3} sin (3 x) + C

Solution steps

\int 1 + cos (3 x) 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 1 d x + \int cos (3 x) d x

\int 1 d x = x

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

= x + \frac{1}{3} sin (3 x)

Add a constant to the solution

= x + \frac{1}{3} sin (3 x) + C

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