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

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

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

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

cos (x) - sin (x) + C

Solution steps

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

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

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

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

Simplify

= cos (x) - sin (x)

Add a constant to the solution

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

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

\int e^{- \frac{1}{4} x} d x

\int 24 x + 24 x^{2} d x

\int x^{\frac{1}{2}} + 3 d x

\int \frac{5 x + 6}{x ^{2} + x + 1} d x

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