What is the integral of e^{-4x^2} ?

The integral of e^{-4x^2} is (sqrt(pi))/4 \erf(sqrt(4)x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-4x^2}

\int e^{- 4 x^{2}} d x

\frac{π}{4} erf (4 x) + C

Solution steps

\int e^{- 4 x^{2}} d x

= \int e^{- (4 x)^{2}} d x

Apply u-substitution

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

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

Use the nonelementary integral:

\int e^{- u^{2}} d u = \frac{π}{2} erf (u)

= \frac{1}{2} \cdot \frac{π}{2} erf (u)

Substitute back

u = 4 x

= \frac{1}{2} \cdot \frac{π}{2} erf (4 x)

Simplify

\frac{1}{2} \cdot \frac{π}{2} erf (4 x) : \frac{π}{4} erf (4 x)

= \frac{π}{4} erf (4 x)

Add a constant to the solution

= \frac{π}{4} erf (4 x) + C

n = 1 \sum \infty (cos (0.3))^{n}

\int \frac{csc ( x )}{csc ( x ) - sin ( x )} d x

\frac{d y}{d t} + y = t e^{t}

f (x) = \frac{1}{2 x}, at x = 36

What is the integral of e^{-4x^2} ?
The integral of e^{-4x^2} is (sqrt(pi))/4 \erf(sqrt(4)x)+C