What is the integral of 1/2 e^{x^2} ?

The integral of 1/2 e^{x^2} is (sqrt(pi))/4 \erfi(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/2 e^{x^2}

\int \frac{1}{2} e^{x^{2}} d x

\frac{π}{4} erfi (x) + C

Solution steps

\int \frac{1}{2} e^{x^{2}} d x

Take the constant out:

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

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

Use the nonelementary integral:

\int e^{x^{2}} d x = \frac{π}{2} erfi (x)

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

Simplify

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

= \frac{π}{4} erfi (x)

Add a constant to the solution

= \frac{π}{4} erfi (x) + C

(x^{2} - 4) \cdot \frac{d y}{d x} + 4 y = (x + 2)^{2}

\int 12 x y d x

x^{2} y^{^{''}} - x y^{^{'}} + 2 y = 0

\frac{d}{d x} (\frac{2 y}{x})

\int 9 sin^{4} (x) cos^{2} (x) d x

What is the integral of 1/2 e^{x^2} ?
The integral of 1/2 e^{x^2} is (sqrt(pi))/4 \erfi(x)+C