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

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

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

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

2 cos (x) + 4 sin (x) + C

Solution steps

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

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

\int 4 cos (x) d x = 4 sin (x)

= - (- 2 cos (x)) + 4 sin (x)

Simplify

= 2 cos (x) + 4 sin (x)

Add a constant to the solution

= 2 cos (x) + 4 sin (x) + C

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

\frac{d}{d x} ((7 - 3 x) (x + 5))

y^{^{'}} + 3 y = cos (x)

4 y^{^{''}} + y^{^{'}} + 8 y = 0

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

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