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

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

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

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

e^{2} \frac{π}{2} erf (x) + C

Solution steps

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

Simplify

e^{- x^{2} + 2} : e^{- x^{2}} e^{2}

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

Take the constant out:

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

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

Use the nonelementary integral:

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

= e^{2} \frac{π}{2} erf (x)

Add a constant to the solution

= e^{2} \frac{π}{2} erf (x) + C

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