What is the integral of cos(2pix) ?

The integral of cos(2pix) is 1/(2pi)sin(2xpi)+C

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integral of cos(2pix)

\int cos (2 π x) d x

\frac{1}{2 π} sin (2 x π) + C

Solution steps

\int cos (2 π x) d x

Apply u-substitution

: \int cos (u) \frac{1}{2 π} d u

= \int cos (u) \frac{1}{2 π} d u

Take the constant out:

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

= \frac{1}{2 π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{2 π} sin (u)

Substitute back

u = 2 x π

= \frac{1}{2 π} sin (2 x π)

Add a constant to the solution

= \frac{1}{2 π} sin (2 x π) + C

\frac{d}{d x} ((x^{5} - 9 x)^{2})

f (x) = 4 x^{3} - 5 x + 1

\frac{\partial}{\partial z} (2 x y + z^{2})

\frac{\partial}{\partial y} (y x^{2})

\int x (x - 2021) d x

What is the integral of cos(2pix) ?
The integral of cos(2pix) is 1/(2pi)sin(2xpi)+C