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

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

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integral of-5sin(x)

\int - 5 sin (x) d x

5 cos (x) + C

Solution steps

\int - 5 sin (x) d x

Take the constant out:

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

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

Use the common integral:

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

= - 5 (- cos (x))

Simplify

= 5 cos (x)

Add a constant to the solution

= 5 cos (x) + C

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