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

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

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

\frac{π}{2} erfi (x) - x + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{x^{2}} d x - \int 1 d x

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

\int 1 d x = x

= \frac{π}{2} erfi (x) - x

Add a constant to the solution

= \frac{π}{2} erfi (x) - x + C

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

\int (- \frac{2}{x}) d x

\int \frac{1}{( 2 x - x ^{2} ) ^{3}} d x

\int x^{3} e^{x^{4} + 1} d x

\int \frac{9 x ^{2} + x}{( 12 x ^{3} + 2 x ^{2} ) ^{2}} d x

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