What is the integral of-sin(u) ?

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

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integral of-sin(u)

\int - sin (u) d u

cos (u) + C

Solution steps

\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))

Simplify

= cos (u)

Add a constant to the solution

= cos (u) + C