What is the integral of sin(x/6) ?

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

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integral of sin(x/6)

\int sin (\frac{x}{6}) d x

- 6 cos (\frac{x}{6}) + C

Solution steps

\int sin (\frac{x}{6}) d x

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= 6 (- cos (u))

Substitute back

u = \frac{x}{6}

= 6 (- cos (\frac{x}{6}))

Simplify

= - 6 cos (\frac{x}{6})

Add a constant to the solution

= - 6 cos (\frac{x}{6}) + C