What is the integral of e^{16x^2} ?

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

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integral of e^{16x^2}

\int e^{16 x^{2}} d x

\frac{π}{8} erfi (16 x) + C

Solution steps

\int e^{16 x^{2}} d x

= \int e^{(16 x)^{2}} d x

Apply u-substitution

: \int e^{u^{2}} \frac{1}{4} d u

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

Take the constant out:

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

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

Use the nonelementary integral:

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

= \frac{1}{4} \cdot \frac{π}{2} erfi (u)

Substitute back

u = 16 x

= \frac{1}{4} \cdot \frac{π}{2} erfi (16 x)

Simplify

\frac{1}{4} \cdot \frac{π}{2} erfi (16 x) : \frac{π}{8} erfi (16 x)

= \frac{π}{8} erfi (16 x)

Add a constant to the solution

= \frac{π}{8} erfi (16 x) + C

\int_{- 1}^{x^{2}} (- 2 t + 2) d t

\frac{5}{x}

\frac{1}{e ^{y}}

y = \frac{- 2 y + x + 2}{2 y - x + 4}, (- 3, - 1)

f (x) = - sin (3 x) \cdot 3

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