What is the integral of 1/4096 cos(8x) ?

The integral of 1/4096 cos(8x) is 1/32768 sin(8x)+C

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integral of 1/4096 cos(8x)

\int \frac{1}{4096} cos (8 x) d x

\frac{1}{32768} sin (8 x) + C

Solution steps

\int \frac{1}{4096} cos (8 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4096} \cdot \int cos (8 x) d x

Apply u-substitution

: \int cos (u) \frac{1}{8} d u

= \frac{1}{4096} \cdot \int cos (u) \frac{1}{8} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4096} \cdot \frac{1}{8} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{4096} \cdot \frac{1}{8} sin (u)

Substitute back

u = 8 x

= \frac{1}{4096} \cdot \frac{1}{8} sin (8 x)

Simplify

\frac{1}{4096} \cdot \frac{1}{8} sin (8 x) : \frac{1}{32768} sin (8 x)

= \frac{1}{32768} sin (8 x)

Add a constant to the solution

= \frac{1}{32768} sin (8 x) + C

\frac{e ^{- 2 s}}{s - 1}

\frac{d y}{d t} = \frac{2}{t} y + t^{3} e^{t}

\int 3^{- 6 x} d x

\frac{3}{s ( s ^{2} + 2 s + 4 )}

What is the integral of 1/4096 cos(8x) ?
The integral of 1/4096 cos(8x) is 1/32768 sin(8x)+C