What is the integral of-5sin(t) ?

The integral of-5sin(t) is 5cos(t)+C

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integral of-5sin(t)

\int - 5 sin (t) d t

5 cos (t) + C

Solution steps

\int - 5 sin (t) d t

Take the constant out:

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

= - 5 \cdot \int sin (t) d t

Use the common integral:

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

= - 5 (- cos (t))

Simplify

= 5 cos (t)

Add a constant to the solution

= 5 cos (t) + C

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