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

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

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integral of cos(3-x)

\int cos (3 - x) d x

- sin (3 - x) + C

Solution steps

\int cos (3 - x) d x

Apply u-substitution

: \int - cos (u) d u

= \int - cos (u) d u

Take the constant out:

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

= - \int cos (u) d u

Use the common integral:

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

= - sin (u)

Substitute back

u = 3 - x

= - sin (3 - x)

Add a constant to the solution

= - sin (3 - x) + C

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