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

The integral of cos(x/a) is asin(x/a)+C

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integral of cos(x/a)

\int cos (\frac{x}{a}) d x

a sin (\frac{x}{a}) + C

Solution steps

\int cos (\frac{x}{a}) d x

Apply u-substitution

= \int cos (u) a d u

Take the constant out:

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

= a \cdot \int cos (u) d u

Use the common integral:

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

= a sin (u)

Substitute back

u = \frac{x}{a}

= a sin (\frac{x}{a})

Add a constant to the solution

= a sin (\frac{x}{a}) + C