What is the integral of 6sin(x)-3sin(2x) ?

The integral of 6sin(x)-3sin(2x) is -6cos(x)+3/2 cos(2x)+C

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integral of 6sin(x)-3sin(2x)

\int 6 sin (x) - 3 sin (2 x) d x

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

Solution steps

\int 6 sin (x) - 3 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 6 sin (x) d x - \int 3 sin (2 x) d x

\int 6 sin (x) d x = - 6 cos (x)

\int 3 sin (2 x) d x = - \frac{3}{2} cos (2 x)

= - 6 cos (x) - (- \frac{3}{2} cos (2 x))

Simplify

= - 6 cos (x) + \frac{3}{2} cos (2 x)

Add a constant to the solution

= - 6 cos (x) + \frac{3}{2} cos (2 x) + C

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What is the integral of 6sin(x)-3sin(2x) ?
The integral of 6sin(x)-3sin(2x) is -6cos(x)+3/2 cos(2x)+C