Integrals of the form
or
can be evaluated instantly. For example,
When the integrand is tow multiple and trigonometric terms multiplied together, we must use a trigonometric identity to express the integrand as the sum of two trigonometric terms using the identities
(1)
(2)
(3)
(4)
each term of which can be integrated separately.
To evaluate
for example use (4). The integral becomes
To evaluate
use (2). The integral becomes
To evaluate int cos 3x cos 5x dx use (3). The integral becomes
To evaluate
use (1). The integral becomes
