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

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

x \to 1 lim ((x - 1)^{(x + 4)})

(2 x y^{2} - 6) d x + (2 x^{2} y + 7) d y = 0

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

x^{3} y^{2} = x y^{3} + 6

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