What is the integral of 6sin(6s) ?

The integral of 6sin(6s) is -cos(6s)+C

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integral of 6sin(6s)

\int 6 sin (6 s) d s

- cos (6 s) + C

Solution steps

\int 6 sin (6 s) d s

Take the constant out:

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

= 6 \cdot \int sin (6 s) d s

Apply u-substitution

: \int sin (u) \frac{1}{6} d u

= 6 \cdot \int sin (u) \frac{1}{6} d u

Take the constant out:

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

= 6 \cdot \frac{1}{6} \cdot \int sin (u) d u

Use the common integral:

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

= 6 \cdot \frac{1}{6} (- cos (u))

Substitute back

u = 6 s

= 6 \cdot \frac{1}{6} (- cos (6 s))

Simplify

6 \cdot \frac{1}{6} (- cos (6 s)) : - cos (6 s)

= - cos (6 s)

Add a constant to the solution

= - cos (6 s) + C

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