What is the integral from x to x^3 of e^{t^2} ?

The integral from x to x^3 of e^{t^2} is (sqrt(pi))/2 \erfi(x^3)-(sqrt(pi))/2 \erfi(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from x to x^3 of e^{t^2}

\int_{x}^{x^{3}} e^{t^{2}} d t

\frac{π}{2} erfi (x^{3}) - \frac{π}{2} erfi (x)

Solution steps

\int_{x}^{x^{3}} e^{t^{2}} d t

Use the nonelementary integral:

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

= [\frac{π}{2} erfi (t)]_{x}^{x^{3}}

Compute the boundaries:

\frac{π}{2} erfi (x^{3}) - \frac{π}{2} erfi (x)

= \frac{π}{2} erfi (x^{3}) - \frac{π}{2} erfi (x)

\int_{0}^{2} 4 - y^{2} d y

\int_{0}^{1} 3^{5 x} d x

\int_{0}^{6} (3 x^{2} + 1) d x

\int_{1}^{32} x^{- \frac{4}{5}} d x

\int_{2}^{- 2} (9 r + 8)^{2} d r

What is the integral from x to x^3 of e^{t^2} ?
The integral from x to x^3 of e^{t^2} is (sqrt(pi))/2 \erfi(x^3)-(sqrt(pi))/2 \erfi(x)