What is the integral of cos(6x)cos(5x) ?

The integral of cos(6x)cos(5x) is 1/2 (1/11 sin(11x)+sin(x))+C

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integral of cos(6x)cos(5x)

\int cos (6 x) cos (5 x) d x

\frac{1}{2} (\frac{1}{11} sin (11 x) + sin (x)) + C

Solution steps

\int cos (6 x) cos (5 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (cos (11 x) + cos (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 (11 x) + cos (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 (11 x) d x + \int cos (x) d x)

\int cos (11 x) d x = \frac{1}{11} sin (11 x)

\int cos (x) d x = sin (x)

= \frac{1}{2} (\frac{1}{11} sin (11 x) + sin (x))

Add a constant to the solution

= \frac{1}{2} (\frac{1}{11} sin (11 x) + sin (x)) + C

g (t) = \frac{t - t}{t ^{\frac{1}{5}}}

\frac{d y}{d x} = \frac{( 2 cos ( 2 x ) )}{3 + 2 y}

x \to \infty lim (\frac{1}{2 x})

\frac{d}{d x} (ln (ln (2 x^{3})))

\frac{\partial}{\partial y} ((x + y) e^{x})

What is the integral of cos(6x)cos(5x) ?
The integral of cos(6x)cos(5x) is 1/2 (1/11 sin(11x)+sin(x))+C