What is the integral of e^{-r^2} ?

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

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integral of e^{-r^2}

\int e^{- r^{2}} d r

\frac{π}{2} erf (r) + C

Solution steps

\int e^{- r^{2}} d r

Use the nonelementary integral:

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

= \frac{π}{2} erf (r)

Add a constant to the solution

= \frac{π}{2} erf (r) + C

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

\int e^{- r} d r

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\int 4 4 - x^{2} d x

\int (x^{2} - 2) x^{3} - 6 x + 3 d x

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