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

The integral from-1 to 1 of x^2e^{x^2} is e+(-sqrt(pi)\erfi(1)+sqrt(pi)\erfi(-1))/4

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

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

e + \frac{- π erfi ( 1 ) + π erfi ( - 1 )}{4}

Solution steps

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

Simplify

x^{2} : xx

= \int_{- 1}^{1} xx e^{x^{2}} d x

Apply Integration By Parts

= [\frac{1}{2} e^{x^{2}} x - \int \frac{1}{2} e^{x^{2}} d x]_{- 1}^{1}

\int \frac{1}{2} e^{x^{2}} d x = \frac{π}{4} erfi (x)

= [\frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x)]_{- 1}^{1}

Compute the boundaries:

e + \frac{- π erfi ( 1 ) + π erfi ( - 1 )}{4}

= e + \frac{- π erfi ( 1 ) + π erfi ( - 1 )}{4}

What is the integral from-1 to 1 of x^2e^{x^2} ?
The integral from-1 to 1 of x^2e^{x^2} is e+(-sqrt(pi)\erfi(1)+sqrt(pi)\erfi(-1))/4