You should convert the product in sum such that:

`sin(5x) cos(2x) = (1/2)(sin (5x - 2x) + sin(5x + 2x))`

Hence, evaluating the integral yields:

`int sin(5x) cos(2x) dx= (1/2)int (sin (3x) + sin(7x)) dx`

Using the linearity yields:

`int sin(5x) cos(2x) dx = (1/2)int (sin (3x)) dx + (1/2) int (sin(7x)) dx`

`int sin(5x) cos(2x) dx = (1/2)(-(cos(3x))/3 - (cos(7x))/7) + c`

**Hence, evluating the given integral yields `int sin(5x) cos(2x) dx = (1/2)(-(cos(3x))/3 - (cos(7x))/7) + c.` **