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Integrating Products of Multiple Angle Trigonometric Functions

Integrals of the formorcan 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 evaluatefor example use (4). The integral becomes

To evaluateuse (2). The integral becomes

To evaluate int cos 3x cos 5x dx use (3). The integral becomes

To evaluateuse (1). The integral becomes