What is the integral of 1/(e^{x^2)} ?

The integral of 1/(e^{x^2)} is (sqrt(pi))/2 \erf(x)+C

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integral of 1/(e^{x^2)}

\int \frac{1}{e ^{x^{2}}} d x

\frac{π}{2} erf (x) + C

Solution steps

\int \frac{1}{e ^{x^{2}}} d x

Apply exponent rule:

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

\frac{1}{e ^{x^{2}}} = e^{- x^{2}}

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

Use the nonelementary integral:

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

= \frac{π}{2} erf (x)

Add a constant to the solution

= \frac{π}{2} erf (x) + C

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What is the integral of 1/(e^{x^2)} ?
The integral of 1/(e^{x^2)} is (sqrt(pi))/2 \erf(x)+C