What is the integral of sin(4pix) ?

The integral of sin(4pix) is -1/(4pi)cos(4pix)+C

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integral of sin(4pix)

\int sin (4 π x) d x

- \frac{1}{4 π} cos (4 π x) + C

Solution steps

\int sin (4 π x) d x

Apply u-substitution

: \int sin (u) \frac{1}{4 π} d u

= \int sin (u) \frac{1}{4 π} d u

Take the constant out:

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

= \frac{1}{4 π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{4 π} (- cos (u))

Substitute back

u = 4 π x

= \frac{1}{4 π} (- cos (4 π x))

Simplify

= - \frac{1}{4 π} cos (4 π x)

Add a constant to the solution

= - \frac{1}{4 π} cos (4 π x) + C

\int \frac{2}{( x - 2 ) ^{3}} d x

cos (3 x), 0

\int_{1}^{4} 2 e^{x} d x

- 9 t^{2} + 18 t + 7

y^{^{'}} + 2 y = 35 sin (t) + 35 cos (t)

What is the integral of sin(4pix) ?
The integral of sin(4pix) is -1/(4pi)cos(4pix)+C