What is the integral of 21xe^{-11x^2} ?

The integral of 21xe^{-11x^2} is -21/22 e^{-11x^2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 21xe^{-11x^2}

\int 21 x e^{- 11 x^{2}} d x

- \frac{21}{22} e^{- 11 x^{2}} + C

Solution steps

\int 21 x e^{- 11 x^{2}} d x

Take the constant out:

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

= 21 \cdot \int x e^{- 11 x^{2}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{22} d u

= 21 \cdot \int - \frac{e ^{u}}{22} d u

Take the constant out:

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

= 21 (- \frac{1}{22} \cdot \int e^{u} d u)

Use the common integral:

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

= 21 (- \frac{1}{22} e^{u})

Substitute back

u = - 11 x^{2}

= 21 (- \frac{1}{22} e^{- 11 x^{2}})

Simplify

21 (- \frac{1}{22} e^{- 11 x^{2}}) : - \frac{21}{22} e^{- 11 x^{2}}

= - \frac{21}{22} e^{- 11 x^{2}}

Add a constant to the solution

= - \frac{21}{22} e^{- 11 x^{2}} + C

\int \frac{x + y}{x - y} d x

\int 6 x x - 8 d x

\frac{x}{5}

\int \frac{cos ( 2 x )}{sin ( 2 x ) cos ( 2 x )} d x

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

What is the integral of 21xe^{-11x^2} ?
The integral of 21xe^{-11x^2} is -21/22 e^{-11x^2}+C