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

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

Popular >

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int x^{3} (1 + 2 x^{2})^{\frac{- 3}{2}} d x

\int (sin (4 x)) e^{x} d x

\int 6 x - 8 d x

\int \frac{x ^{2} + 2 x}{4 e ^{x + 1}} d x

\int (x^{2} + 3) e^{2 x - 3} d x

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