Calculus Examples

$2 e^{x^{2}}$

Step 1

Write $2 e^{x^{2}}$ as a function.

$f (x) = 2 e^{x^{2}}$

Step 2

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 3

Set up the integral to solve.

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

Step 4

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

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

Step 5

$\int e^{x^{2}} d x$ is a special integral. The integral is the imaginary error function.

$2 (erfi (x) + C)$

Step 6

Simplify.

$2 erfi (x) + C$

Step 7

The answer is the antiderivative of the function $f (x) = 2 e^{x^{2}}$ .

$F (x) =$ $2 erfi (x) + C$