What is the integral of sin(pi/3 x) ?

The integral of sin(pi/3 x) is -3/pi cos(pi/3 x)+C

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integral of sin(pi/3 x)

\int sin (\frac{π}{3} x) d x

- \frac{3}{π} cos (\frac{π}{3} x) + C

Solution steps

\int sin (\frac{π}{3} x) d x

Apply u-substitution

= \int sin (u) \frac{3}{π} d u

Take the constant out:

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

= \frac{3}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{3}{π} (- cos (u))

Substitute back

u = \frac{π}{3} x

= \frac{3}{π} (- cos (\frac{π}{3} x))

Simplify

= - \frac{3}{π} cos (\frac{π}{3} x)

Add a constant to the solution

= - \frac{3}{π} cos (\frac{π}{3} x) + C

What is the integral of sin(pi/3 x) ?
The integral of sin(pi/3 x) is -3/pi cos(pi/3 x)+C