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

The integral of e^{4x^2} is (sqrt(pi))/4 \erfi(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} erfi (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} erfi (u)

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

Substitute back

u = 4 x

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

Simplify

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

= \frac{π}{4} erfi (4 x)

Add a constant to the solution

= \frac{π}{4} erfi (4 x) + C

\frac{d x}{d y} = \frac{x}{y}

\frac{\partial}{\partial y} (\frac{18 x y}{x + y})

arccsc (x^{4} + 1)

n \to \infty lim (2^{\frac{1}{n}})

y^{^{'}} + e^{x} y = e^{3 x} y^{- 2}

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