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

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

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

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

cos (2 x) + sin (2 x) + C

Solution steps

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

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

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

= - (- cos (2 x)) + sin (2 x)

Simplify

= cos (2 x) + sin (2 x)

Add a constant to the solution

= cos (2 x) + sin (2 x) + C

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