What is the integral of e^{cos(8x)}sin(8x) ?

The integral of e^{cos(8x)}sin(8x) is -1/8 e^{cos(8x)}+C

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integral of e^{cos(8x)}sin(8x)

\int e^{c o s (8 x)} sin (8 x) d x

- \frac{1}{8} e^{c o s (8 x)} + C

Solution steps

\int e^{c o s (8 x)} sin (8 x) d x

Apply u-substitution

: \int e^{c o s (u)} sin (u) \frac{1}{8} d u

= \int e^{c o s (u)} sin (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}{8} \cdot \int e^{c o s (u)} sin (u) d u

Apply u-substitution

: \int - e^{v} d v

= \frac{1}{8} \cdot \int - e^{v} d v

Take the constant out:

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

= \frac{1}{8} (- \int e^{v} d v)

Use the common integral:

\int e^{v} d v = e^{v}

= \frac{1}{8} (- e^{v})

Substitute back

= \frac{1}{8} (- e^{c o s (8 x)})

Simplify

= - \frac{1}{8} e^{c o s (8 x)}

Add a constant to the solution

= - \frac{1}{8} e^{c o s (8 x)} + C

x \to 1 lim ((x - 1) (x + 1))

\frac{d}{d x} (\frac{1}{cos ( x )})

x \to 0 lim (x e^{x})

\frac{d}{d x} ((\frac{x - 5}{2 x + 1})^{3})

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

What is the integral of e^{cos(8x)}sin(8x) ?
The integral of e^{cos(8x)}sin(8x) is -1/8 e^{cos(8x)}+C