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人気のある微分積分 >

integral from x to x^5 of e^{t^2}

解

\int_{x}^{x^{5}} e^{t^{2}} d t

解

\frac{π}{2} erfi (x^{5}) - \frac{π}{2} erfi (x)

解答ステップ

\int_{x}^{x^{5}} e^{t^{2}} d t

非初等積分を使用する:

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

= [\frac{π}{2} erfi (t)]_{x}^{x^{5}}

限度を計算する:

\frac{π}{2} erfi (x^{5}) - \frac{π}{2} erfi (x)

= \frac{π}{2} erfi (x^{5}) - \frac{π}{2} erfi (x)

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