What is the integral of 3sin(3s) ?

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

integral of 3sin(3s)

\int 3 sin (3 s) d s

- cos (3 s) + C

Solution steps

\int 3 sin (3 s) d s

Take the constant out:

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

= 3 \cdot \int sin (3 s) d s

Apply u-substitution

= 3 \cdot \int sin (u) \frac{1}{3} d u

Take the constant out:

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

= 3 \cdot \frac{1}{3} \cdot \int sin (u) d u

Use the common integral:

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

= 3 \cdot \frac{1}{3} (- cos (u))

Substitute back

u = 3 s

= 3 \cdot \frac{1}{3} (- cos (3 s))

Simplify

3 \cdot \frac{1}{3} (- cos (3 s)) : - cos (3 s)

= - cos (3 s)

Add a constant to the solution

= - cos (3 s) + C

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