What is the integral of sin(1/5 x) ?

The integral of sin(1/5 x) is -5cos(1/5 x)+C

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integral of sin(1/5 x)

\int sin (\frac{1}{5} x) d x

- 5 cos (\frac{1}{5} x) + C

Solution steps

\int sin (\frac{1}{5} x) d x

Apply u-substitution

: \int sin (u) \cdot 5 d u

= \int sin (u) \cdot 5 d u

Take the constant out:

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

= 5 \cdot \int sin (u) d u

Use the common integral:

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

= 5 (- cos (u))

Substitute back

u = \frac{1}{5} x

= 5 (- cos (\frac{1}{5} x))

Simplify

= - 5 cos (\frac{1}{5} x)

Add a constant to the solution

= - 5 cos (\frac{1}{5} x) + C

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What is the integral of sin(1/5 x) ?
The integral of sin(1/5 x) is -5cos(1/5 x)+C