What is the integral of e^{(t^2)/4} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{(t^2)/4}

\int e^{\frac{t ^{2}}{4}} d t

π erfi (\frac{t}{2}) + C

Solution steps

\int e^{\frac{t ^{2}}{4}} d t

Apply exponent rule:

\frac{a ^{n}}{b ^{n}} = (\frac{a}{b})^{n}

\frac{t ^{2}}{4} = (\frac{t}{2})^{2}

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

Apply u-substitution

: \int e^{u^{2}} \cdot 2 d u

= \int e^{u^{2}} \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int e^{u^{2}} d u

Use the nonelementary integral:

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

= 2 \cdot \frac{π}{2} erfi (u)

Substitute back

u = \frac{t}{2}

= 2 \cdot \frac{π}{2} erfi (\frac{t}{2})

Simplify

2 \cdot \frac{π}{2} erfi (\frac{t}{2}) : π erfi (\frac{t}{2})

= π erfi (\frac{t}{2})

Add a constant to the solution

= π erfi (\frac{t}{2}) + C

\int 18 sin (x) d x

\int (- 4 cos (x)) d x

\int \frac{x}{1 - x cot ( x )} d x

\int \frac{2 x}{3 x ^{2} + 1} d x

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

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