What is the integral of sin(30x) ?

The integral of sin(30x) is -1/30 cos(30x)+C

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integral of sin(30x)

\int sin (30 x) d x

- \frac{1}{30} cos (30 x) + C

Solution steps

\int sin (30 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{30} d u

= \int sin (u) \frac{1}{30} d u

Take the constant out:

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

= \frac{1}{30} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{30} (- cos (u))

Substitute back

u = 30 x

= \frac{1}{30} (- cos (30 x))

Simplify

= - \frac{1}{30} cos (30 x)

Add a constant to the solution

= - \frac{1}{30} cos (30 x) + C

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