What is the integral of (sin(x)-8cos(x)) ?

The integral of (sin(x)-8cos(x)) is -cos(x)-8sin(x)+C

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integral of (sin(x)-8cos(x))

\int (sin (x) - 8 cos (x)) d x

- cos (x) - 8 sin (x) + C

Solution steps

\int sin (x) - 8 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 8 cos (x) d x

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

\int 8 cos (x) d x = 8 sin (x)

= - cos (x) - 8 sin (x)

Add a constant to the solution

= - cos (x) - 8 sin (x) + C

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\int_{0}^{1} \frac{1}{x ^{2} - 3} d x

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\frac{\partial}{\partial y} (x y e^{s i n (π x y)})

What is the integral of (sin(x)-8cos(x)) ?
The integral of (sin(x)-8cos(x)) is -cos(x)-8sin(x)+C