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

The integral of cos(x)cos(nx) is 1/2 (1/(1+n)sin(x+nx)+1/(1-n)sin(x-nx))+C

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integral of cos(x)cos(nx)

\int cos (x) cos (n x) d x

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

Solution steps

\int cos (x) cos (n x) d x

Rewrite using trig identities

= \int \frac{cos ( x + n x ) + cos ( x - n x )}{2} 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 (x + n x) + cos (x - n 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 (x + n x) d x + \int cos (x - n x) d x)

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

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

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

Add a constant to the solution

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

\frac{\partial}{\partial x} ((1 + \frac{2}{y}) sin (x))

\int \frac{e ^{x}}{( 4 + 9 e ^{2 x} )} d x

\frac{1}{s} \cdot \frac{1}{s ^{2} + \frac{s}{2} + \frac{1}{2}}

\int \frac{1}{x ^{2} + 8 x + 52} d x

x^{2} y^{^{'}} = y^{2} + 3 x y

What is the integral of cos(x)cos(nx) ?
The integral of cos(x)cos(nx) is 1/2 (1/(1+n)sin(x+nx)+1/(1-n)sin(x-nx))+C