What is the integral of (sin(x)-3cos(x)) ?

The integral of (sin(x)-3cos(x)) is -cos(x)-3sin(x)+C

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integral of (sin(x)-3cos(x))

\int (sin (x) - 3 cos (x)) d x

- cos (x) - 3 sin (x) + C

Solution steps

\int sin (x) - 3 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 3 cos (x) d x

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

\int 3 cos (x) d x = 3 sin (x)

= - cos (x) - 3 sin (x)

Add a constant to the solution

= - cos (x) - 3 sin (x) + C

\int e^{9 x - 2} d x

\frac{\partial}{\partial x} (e^{- 5 y} cos (5 x))

y = \frac{24}{x ^{4}}

\frac{d}{d x} (3 sin^{4} (x))

\frac{d ^{2} x}{d t ^{2}} + a x = 0

What is the integral of (sin(x)-3cos(x)) ?
The integral of (sin(x)-3cos(x)) is -cos(x)-3sin(x)+C