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

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

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integral of e^{x^2-4}

\int e^{x^{2} - 4} d x

\frac{π}{2 e ^{4}} erfi (x) + C

Solution steps

\int e^{x^{2} - 4} d x

Simplify

e^{x^{2} - 4} : e^{x^{2}} e^{- 4}

= \int e^{x^{2}} e^{- 4} d x

Take the constant out:

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

= e^{- 4} \cdot \int e^{x^{2}} d x

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{4}} \cdot \int e^{x^{2}} d x

Use the nonelementary integral:

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

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

Simplify

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

= \frac{π}{2 e ^{4}} erfi (x)

Add a constant to the solution

= \frac{π}{2 e ^{4}} erfi (x) + C

x \to 4 lim (3 - 4)

\int \frac{1}{1 + 16 x} d x

\frac{d y}{d x} - \frac{y}{x} = 7 x e^{x}

\int_{1}^{36} \frac{1}{2 x} d x

x \to - 5 lim (3 x + 2)

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