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

解答

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

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

求解步骤

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

这是非初等函数积分:

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

= [\frac{π}{2} erfi (t)]_{1}^{x}

带入上下限计算后得:

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

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

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