Calculus Examples

$\frac{1}{e^{x^{2}}}$

Step 1

Negate the exponent of $e^{x^{2}}$ and move it out of the denominator.

$\int 1 {(e^{x^{2}})}^{- 1} d x$

Step 2

Simplify.

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Step 2.1

Multiply the exponents in ${(e^{x^{2}})}^{- 1}$ .

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Step 2.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\int 1 e^{x^{2} \cdot - 1} d x$

Step 2.1.2

Move $- 1$ to the left of $x^{2}$ .

$\int 1 e^{- 1 \cdot x^{2}} d x$

Step 2.1.3

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$\int 1 e^{- x^{2}} d x$

Step 2.2

Multiply $e^{- x^{2}}$ by $1$ .

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

Step 3

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

$erf (x) + C$