What is the integral of 1-e^{-x^2} ?

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

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integral of 1-e^{-x^2}

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

x - \frac{π}{2} erf (x) + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d x = x

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

= x - \frac{π}{2} erf (x)

Add a constant to the solution

= x - \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 x-(sqrt(pi))/2 \erf(x)+C