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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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

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\int (- 2)^{x} d x

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