What is the integral of pisin(8pix) ?

The integral of pisin(8pix) is -1/8 cos(8pix)+C

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integral of pisin(8pix)

\int π sin (8 π x) d x

- \frac{1}{8} cos (8 π x) + C

Solution steps

\int π sin (8 π x) d x

Take the constant out:

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

= π \cdot \int sin (8 π x) d x

Apply u-substitution

: \int sin (u) \frac{1}{8 π} d u

= π \cdot \int sin (u) \frac{1}{8 π} d u

Take the constant out:

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

= π \frac{1}{8 π} \cdot \int sin (u) d u

Use the common integral:

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

= π \frac{1}{8 π} (- cos (u))

Substitute back

u = 8 π x

= π \frac{1}{8 π} (- cos (8 π x))

Simplify

π \frac{1}{8 π} (- cos (8 π x)) : - \frac{1}{8} cos (8 π x)

= - \frac{1}{8} cos (8 π x)

Add a constant to the solution

= - \frac{1}{8} cos (8 π x) + C

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What is the integral of pisin(8pix) ?
The integral of pisin(8pix) is -1/8 cos(8pix)+C