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

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

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

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

sin (x) + cos (x) + C

Solution steps

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

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

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

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

Simplify

= sin (x) + cos (x)

Add a constant to the solution

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

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