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

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

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integral of (3-sin(x))

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

3 x + cos (x) + C

Solution steps

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

\int 3 d x = 3 x

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

= 3 x - (- cos (x))

Simplify

= 3 x + cos (x)

Add a constant to the solution

= 3 x + cos (x) + C

\int_{0}^{7} x e^{- 2 x} d x

\frac{d}{d x} (64 sin (2 x))

\frac{d}{d x} (sec^{9} (2^{x}))

x^{- 8}

\frac{\partial}{\partial x} (e^{(3 x + 5 y)})