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

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

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integral of sin(2x)+1

\int sin (2 x) + 1 d x

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

Solution steps

\int sin (2 x) + 1 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 sin (2 x) d x + \int 1 d x

\int sin (2 x) d x = - \frac{1}{2} cos (2 x)

\int 1 d x = x

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

Add a constant to the solution

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

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