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

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

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integral of sin(3-x)

\int sin (3 - x) d x

cos (3 - x) + C

Solution steps

\int sin (3 - x) d x

Apply u-substitution

: \int - sin (u) d u

= \int - sin (u) d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int sin (u) d u

Use the common integral:

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

= - (- cos (u))

Substitute back

u = 3 - x

= - (- cos (3 - x))

Simplify

= cos (3 - x)

Add a constant to the solution

= cos (3 - x) + C

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