What is the integral of e^{(8x)^2} ?

The integral of e^{(8x)^2} is (sqrt(pi))/(16)\erfi(8x)+C

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integral of e^{(8x)^2}

integral

e^{(8 x)^{2}}

\frac{π}{16} erfi (8 x) + C

Solution steps

\int e^{(8 x)^{2}} d x

Apply u-substitution

: \int e^{u^{2}} \frac{1}{8} d u

= \int e^{u^{2}} \frac{1}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int e^{u^{2}} d u

Use the nonelementary integral:

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

= \frac{1}{8} \cdot \frac{π}{2} erfi (u)

Substitute back

u = 8 x

= \frac{1}{8} \cdot \frac{π}{2} erfi (8 x)

Simplify

\frac{1}{8} \cdot \frac{π}{2} erfi (8 x) : \frac{π}{16} erfi (8 x)

= \frac{π}{16} erfi (8 x)

Add a constant to the solution

= \frac{π}{16} erfi (8 x) + C

ln (1 - x)

\frac{( 2 x + 4 )}{( x ^{3} - 1 )}

(x^{2} + 5) \cdot 2^{x}

2 e^{- 2} x

3 x^{2} + 2 x + 1

What is the integral of e^{(8x)^2} ?
The integral of e^{(8x)^2} is (sqrt(pi))/(16)\erfi(8x)+C