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

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

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integral of e^{1-x^2}

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

e \frac{π}{2} erf (x) + C

Solution steps

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

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

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Simplify

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

Use the nonelementary integral:

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

= e \frac{π}{2} erf (x)

Add a constant to the solution

= e \frac{π}{2} erf (x) + C

\int (3 e^{x} - \frac{1}{3} x^{3}) d x

\int 13 x e^{- x^{2}} d x

\frac{\partial}{\partial x} (2 x^{3} y + sin (x^{4}))

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

\frac{d}{d y} (3 x e^{- \frac{1}{y ^{3}}} - 20 x^{3})

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