What is the integral of sin(4x)-cos(2x) ?

The integral of sin(4x)-cos(2x) is -1/4 cos(4x)-1/2 sin(2x)+C

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integral of sin(4x)-cos(2x)

\int sin (4 x) - cos (2 x) d x

- \frac{1}{4} cos (4 x) - \frac{1}{2} sin (2 x) + C

Solution steps

\int sin (4 x) - cos (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 (4 x) d x - \int cos (2 x) d x

\int sin (4 x) d x = - \frac{1}{4} cos (4 x)

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

= - \frac{1}{4} cos (4 x) - \frac{1}{2} sin (2 x)

Add a constant to the solution

= - \frac{1}{4} cos (4 x) - \frac{1}{2} sin (2 x) + C

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What is the integral of sin(4x)-cos(2x) ?
The integral of sin(4x)-cos(2x) is -1/4 cos(4x)-1/2 sin(2x)+C