What is the integral of sin(2pix) ?

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

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integral of sin(2pix)

\int sin (2 π x) d x

- \frac{1}{2 π} cos (2 π x) + C

Solution steps

\int sin (2 π x) d x

Apply u-substitution

: \int sin (u) \frac{1}{2 π} d u

= \int sin (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 sin (u) d u

Use the common integral:

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

= \frac{1}{2 π} (- cos (u))

Substitute back

u = 2 π x

= \frac{1}{2 π} (- cos (2 π x))

Simplify

= - \frac{1}{2 π} cos (2 π x)

Add a constant to the solution

= - \frac{1}{2 π} cos (2 π x) + C

\frac{d}{d x} (3 x^{2} - 6 x + 10)

1 - 2 x y^{^{'}} = (4 + y^{2})

g (x) = 5

e^{7 x}

f (x) = ln (324 sin^{2} (x))

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