What is the integral of cos((xy)/2) ?

The integral of cos((xy)/2) is 2/x sin((xy)/2)+C

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integral of cos((xy)/2)

\int cos (\frac{x y}{2}) d y

\frac{2}{x} sin (\frac{x y}{2}) + C

Solution steps

\int cos (\frac{x y}{2}) d y

Apply u-substitution

= \int \frac{2 cos ( u )}{x} d u

Take the constant out:

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

= \frac{2}{x} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{2}{x} sin (u)

Substitute back

u = \frac{x y}{2}

= \frac{2}{x} sin (\frac{x y}{2})

Add a constant to the solution

= \frac{2}{x} sin (\frac{x y}{2}) + C

What is the integral of cos((xy)/2) ?
The integral of cos((xy)/2) is 2/x sin((xy)/2)+C