What is the integral of (1-sin(x)) ?

The integral of (1-sin(x)) is x+cos(x)+C

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integral of (1-sin(x))

\int (1 - sin (x)) d x

x + cos (x) + C

Solution steps

\int 1 - 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 1 d x - \int sin (x) d x

\int 1 d x = x

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

= x - (- cos (x))

Simplify

= x + cos (x)

Add a constant to the solution

= x + cos (x) + C