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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{2 s}{s ^{2} + 4}

y = ln (8 - 3 x)

\int e^{- u} u d u

x sin (\frac{8}{x})

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

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