What is the integral of sin(-u+3t) ?

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

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integral of sin(-u+3t)

integral

sin (- u + 3 t)

cos (- u + 3 t) + C

Solution steps

\int sin (- u + 3 t) d u

Apply u-substitution

= \int - sin (v) d v

Take the constant out:

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

= - \int sin (v) d v

Use the common integral:

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

= - (- cos (v))

Substitute back

v = - u + 3 t

= - (- cos (- u + 3 t))

Simplify

= cos (- u + 3 t)

Add a constant to the solution

= cos (- u + 3 t) + C