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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-x^2+3}x

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

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

Solution steps

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

Apply u-substitution

: \int - \frac{e ^{u}}{2} d u

= \int - \frac{e ^{u}}{2} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{2} e^{u}

Substitute back

u = - x^{2} + 3

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

Add a constant to the solution

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

\int \frac{1}{x ^{2} - 5 x - 6} d x

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

\int \frac{ln ( x )}{x \cdot 1 + ln ( x )} d x

\int \frac{2 x + 7}{x ^{2} + 7 x + 2} d x

\int \frac{x}{x - 12} d x

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