What is the integral of sin(6pix) ?

The integral of sin(6pix) is -1/(6pi)cos(6pix)+C

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integral of sin(6pix)

\int sin (6 π x) d x

- \frac{1}{6 π} cos (6 π x) + C

Solution steps

\int sin (6 π x) d x

Apply u-substitution

: \int sin (u) \frac{1}{6 π} d u

= \int sin (u) \frac{1}{6 π} d u

Take the constant out:

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

= \frac{1}{6 π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{6 π} (- cos (u))

Substitute back

u = 6 π x

= \frac{1}{6 π} (- cos (6 π x))

Simplify

= - \frac{1}{6 π} cos (6 π x)

Add a constant to the solution

= - \frac{1}{6 π} cos (6 π x) + C

\frac{\partial}{\partial x} (ln (\frac{2}{x}))

x^{2} y^{^{''}} + x y^{^{'}} - y = 2 x

- \frac{6}{x ^{7}}

\int \frac{1}{( x - 1 ) ( x - 3 )} d x

\frac{d}{d x} (sin (\frac{3}{x}))

What is the integral of sin(6pix) ?
The integral of sin(6pix) is -1/(6pi)cos(6pix)+C