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

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

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integral of cos((pix)/a)

\int cos (\frac{π x}{a}) d x

\frac{a}{π} sin (\frac{π x}{a}) + C

Solution steps

\int cos (\frac{π x}{a}) d x

Apply u-substitution

: \int \frac{a cos ( u )}{π} d u

= \int \frac{a cos ( u )}{π} d u

Take the constant out:

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

= \frac{a}{π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{a}{π} sin (u)

Substitute back

u = \frac{π x}{a}

= \frac{a}{π} sin (\frac{π x}{a})

Add a constant to the solution

= \frac{a}{π} sin (\frac{π x}{a}) + C

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