What is the integral of cos(3x)cos(x) ?

The integral of cos(3x)cos(x) is 1/2 (1/4 sin(4x)+1/2 sin(2x))+C

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integral of cos(3x)cos(x)

\int cos (3 x) cos (x) d x

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

Solution steps

\int cos (3 x) cos (x) d x

Rewrite using trig identities

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

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

\int cos (2 x) d x = \frac{1}{2} sin (2 x)

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{1}{4 n}

d er i v a t i v e (t - 2)^{2}

x \to c lim (\frac{x - c}{2 x - 2 c})

\int - \frac{2}{t} d t

\int \frac{1}{π x ( 1 - x )} d x

What is the integral of cos(3x)cos(x) ?
The integral of cos(3x)cos(x) is 1/2 (1/4 sin(4x)+1/2 sin(2x))+C