What is the integral of sin((pix)/3) ?

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

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integral of sin((pix)/3)

\int sin (\frac{π x}{3}) d x

- \frac{3}{π} cos (\frac{π x}{3}) + C

Solution steps

\int sin (\frac{π x}{3}) d x

Apply u-substitution

: \int sin (u) \frac{3}{π} d u

= \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 x}{3}

= \frac{3}{π} (- cos (\frac{π x}{3}))

Simplify

= - \frac{3}{π} cos (\frac{π x}{3})

Add a constant to the solution

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

(x + y)^{2} d x + (2 x y + x^{2} - 7) d y = 0

1 - x^{2}, x^{2} - 1

f (x) = 2 x^{2} + 4 x + 3

(t^{2} + 25) \frac{d y}{d t} + 2 t y = t^{2} (t^{2} + 25)

\frac{( 2 s + 2.5 )}{( s + 0.5 )}

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