What is the integral of cos(2x)cos(24x) ?

The integral of cos(2x)cos(24x) is 1/2 (1/22 sin(22x)+1/26 sin(26x))+C

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integral of cos(2x)cos(24x)

\int cos (2 x) cos (24 x) d x

\frac{1}{2} (\frac{1}{22} sin (22 x) + \frac{1}{26} sin (26 x)) + C

Solution steps

\int cos (2 x) cos (24 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (cos (26 x) + cos (- 22 x)) 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 (26 x) + cos (- 22 x) d x

Simplify

cos (26 x) + cos (- 22 x) : cos (22 x) + cos (26 x)

= \frac{1}{2} \cdot \int cos (22 x) + cos (26 x) 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 (22 x) d x + \int cos (26 x) d x)

\int cos (22 x) d x = \frac{1}{22} sin (22 x)

\int cos (26 x) d x = \frac{1}{26} sin (26 x)

= \frac{1}{2} (\frac{1}{22} sin (22 x) + \frac{1}{26} sin (26 x))

Add a constant to the solution

= \frac{1}{2} (\frac{1}{22} sin (22 x) + \frac{1}{26} sin (26 x)) + C

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What is the integral of cos(2x)cos(24x) ?
The integral of cos(2x)cos(24x) is 1/2 (1/22 sin(22x)+1/26 sin(26x))+C