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

解答

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

\frac{π erfi ( 1 ) - π erfi ( - 1 )}{2}

求解步骤

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

这是非初等函数积分:

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

= [\frac{π}{2} erfi (x)]_{- 1}^{1}

带入上下限计算后得:

\frac{π erfi ( 1 ) - π erfi ( - 1 )}{2}

= \frac{π erfi ( 1 ) - π erfi ( - 1 )}{2}

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

e x p an d \frac{e ^{x} - 2}{( 1 - e ^{- x} ) ^{2}}

\frac{d}{d x} ((x^{2} - 2)^{- 3})

\frac{\partial}{\partial x} (\frac{1}{2 y})

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