What is the integral of xe^{-3x^2+1} ?

The integral of xe^{-3x^2+1} is -1/6 e^{-3x^2+1}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xe^{-3x^2+1}

\int x e^{- 3 x^{2} + 1} d x

- \frac{1}{6} e^{- 3 x^{2} + 1} + C

Solution steps

\int x e^{- 3 x^{2} + 1} d x

Apply u-substitution

: \int - \frac{e ^{u}}{6} d u

= \int - \frac{e ^{u}}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{6} e^{u}

Substitute back

u = - 3 x^{2} + 1

= - \frac{1}{6} e^{- 3 x^{2} + 1}

Add a constant to the solution

= - \frac{1}{6} e^{- 3 x^{2} + 1} + C

\int e cos (x) sin (x) d x

\int - 3 tan (3 t) d t

\int \frac{6}{9 x ^{2} + 1} d x

\int \frac{1}{11 x - 4} d x

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

What is the integral of xe^{-3x^2+1} ?
The integral of xe^{-3x^2+1} is -1/6 e^{-3x^2+1}+C