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)

Add a constant to the solution

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

e^{x^{2} + 1}, 0

\int 2 e^{- 1.5 x} d x

\frac{d}{d x} (\frac{e ^{x}}{x - 1})

\frac{d}{d x} (cos^{5} (3 x))

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

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