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

The integral of e^{-x^2+2}x is -1/2 e^{-x^2+2}+C

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

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

- \frac{1}{2} e^{- x^{2} + 2} + C

Solution steps

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

Apply u-substitution

= \int - \frac{e ^{u}}{2} d u

Take the constant out:

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

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

Use the common integral:

\int e^{u} d u = e^{u}

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

Substitute back

u = - x^{2} + 2

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

Add a constant to the solution

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

What is the integral of e^{-x^2+2}x ?
The integral of e^{-x^2+2}x is -1/2 e^{-x^2+2}+C