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

The integral of cos(x/y) is ysin(x/y)+C

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integral of cos(x/y)

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

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

Solution steps

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

Apply u-substitution

= \int cos (u) y d u

Take the constant out:

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

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

Use the common integral:

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

= y sin (u)

Substitute back

u = \frac{x}{y}

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

Add a constant to the solution

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