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

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

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

d er i v a t i v e - \frac{6}{x ^{7}}

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

x \to 2 lim (\frac{x}{x + 2})

\frac{d}{d x} ((x^{2} + 1)^{3})

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