What is the integral of cos((pix)/l) ?

The integral of cos((pix)/l) is l/pi sin((pix)/l)+C

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integral of cos((pix)/l)

\int cos (\frac{π x}{l}) d x

\frac{l}{π} sin (\frac{π x}{l}) + C

Solution steps

\int cos (\frac{π x}{l}) d x

Apply u-substitution

= \int \frac{l cos ( u )}{π} d u

Take the constant out:

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

= \frac{l}{π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{l}{π} sin (u)

Substitute back

u = \frac{π x}{l}

= \frac{l}{π} sin (\frac{π x}{l})

Add a constant to the solution

= \frac{l}{π} sin (\frac{π x}{l}) + C

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