What is the integral of cos(30x)*cos(4x)*cos(4x) ?

The integral of cos(30x)*cos(4x)*cos(4x) is 1/30 cos^2(4x)sin(30x)+1/6270 (19sin(22x)-11sin(38x))+C

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integral of cos(30x)cos(4x)cos(4x)

\int cos (30 x) \cdot cos (4 x) \cdot cos (4 x) d x

\frac{1}{30} cos^{2} (4 x) sin (30 x) + \frac{1}{6270} (19 sin (22 x) - 11 sin (38 x)) + C

Solution steps

\int cos (30 x) cos (4 x) cos (4 x) d x

Apply Integration By Parts

: \frac{1}{30} cos^{2} (4 x) sin (30 x) - \int - \frac{2}{15} sin (8 x) sin (30 x) d x

= \frac{1}{30} cos^{2} (4 x) sin (30 x) - \int - \frac{2}{15} sin (8 x) sin (30 x) d x

\int - \frac{2}{15} sin (8 x) sin (30 x) d x = - \frac{1}{6270} (19 sin (22 x) - 11 sin (38 x))

= \frac{1}{30} cos^{2} (4 x) sin (30 x) - (- \frac{1}{6270} (19 sin (22 x) - 11 sin (38 x)))

Simplify

= \frac{1}{30} cos^{2} (4 x) sin (30 x) + \frac{1}{6270} (19 sin (22 x) - 11 sin (38 x))

Add a constant to the solution

= \frac{1}{30} cos^{2} (4 x) sin (30 x) + \frac{1}{6270} (19 sin (22 x) - 11 sin (38 x)) + C

y^{^{'}} = x + y, y (0) = 10

\frac{\partial}{\partial v} (u (v, w) + v e^{w})

n = 2 \sum \infty \frac{8}{n ln ( n )}

\frac{d y}{d x} = \frac{e ^{2 x - y}}{e ^{x + y}}

\int \frac{1}{1 - 2 x} - cos (\frac{x}{3}) d x

What is the integral of cos(30x)*cos(4x)*cos(4x) ?
The integral of cos(30x)*cos(4x)*cos(4x) is 1/30 cos^2(4x)sin(30x)+1/6270 (19sin(22x)-11sin(38x))+C