What is the integral of cos(9x-20)cos(5x+20) ?

The integral of cos(9x-20)cos(5x+20) is 1/2 (1/14 sin(14x)+1/4 sin(4x-40))+C

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integral of cos(9x-20)cos(5x+20)

\int cos (9 x - 20) cos (5 x + 20) d x

\frac{1}{2} (\frac{1}{14} sin (14 x) + \frac{1}{4} sin (4 x - 40)) + C

Solution steps

\int cos (9 x - 20) cos (5 x + 20) d x

Rewrite using trig identities

= \int \frac{1}{2} (cos (14 x) + cos (4 x - 40)) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int cos (14 x) + cos (4 x - 40) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int cos (14 x) d x + \int cos (4 x - 40) d x)

\int cos (14 x) d x = \frac{1}{14} sin (14 x)

\int cos (4 x - 40) d x = \frac{1}{4} sin (4 x - 40)

= \frac{1}{2} (\frac{1}{14} sin (14 x) + \frac{1}{4} sin (4 x - 40))

Add a constant to the solution

= \frac{1}{2} (\frac{1}{14} sin (14 x) + \frac{1}{4} sin (4 x - 40)) + C

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What is the integral of cos(9x-20)cos(5x+20) ?
The integral of cos(9x-20)cos(5x+20) is 1/2 (1/14 sin(14x)+1/4 sin(4x-40))+C