What is the integral of cos(t-u) ?

The integral of cos(t-u) is -sin(t-u)+C

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integral of cos(t-u)

\int cos (t - u) d u

- sin (t - u) + C

Solution steps

\int cos (t - u) d u

Apply u-substitution

: \int - cos (v) d v

= \int - cos (v) d v

Take the constant out:

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

= - \int cos (v) d v

Use the common integral:

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

= - sin (v)

Substitute back

v = t - u

= - sin (t - u)

Add a constant to the solution

= - sin (t - u) + C

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