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

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

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integral of (cos(x)+sin(2x))

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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\int 0.3 x d x

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