What is the integral of e^{cos(3x)}sin(3x) ?

The integral of e^{cos(3x)}sin(3x) is -1/3 e^{cos(3x)}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{cos(3x)}sin(3x)

\int e^{c o s (3 x)} sin (3 x) d x

- \frac{1}{3} e^{c o s (3 x)} + C

Solution steps

\int e^{c o s (3 x)} sin (3 x) d x

Apply u-substitution

: \int e^{c o s (u)} sin (u) \frac{1}{3} d u

= \int e^{c o s (u)} sin (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int e^{c o s (u)} sin (u) d u

Apply u-substitution

: \int - e^{v} d v

= \frac{1}{3} \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}{3} (- \int e^{v} d v)

Use the common integral:

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

= \frac{1}{3} (- e^{v})

Substitute back

= \frac{1}{3} (- e^{c o s (3 x)})

Simplify

= - \frac{1}{3} e^{c o s (3 x)}

Add a constant to the solution

= - \frac{1}{3} e^{c o s (3 x)} + C

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

\int y^{2} - 49 d y

\int \frac{( 1 + x ) ^{2}}{x ( 1 + x ^{2} )} d x

\int e^{- x} sin (\frac{x}{2}) d x

\int \frac{e ^{x}}{e ^{x} - e ^{- x}} d x

What is the integral of e^{cos(3x)}sin(3x) ?
The integral of e^{cos(3x)}sin(3x) is -1/3 e^{cos(3x)}+C