integral from-1 to 1 of e^{x^4}

解

\int_{- 1}^{1} e^{x^{4}} d x

- \frac{1 \cdot Γ ( \frac{1}{4} , - 1 ^{4} )}{4 4 - 1 ^{4}} - - \frac{( - 1 ) Γ ( \frac{1}{4} , - ( - 1 ) ^{4} )}{4 4 - ( - 1 ) ^{4}}

解答ステップ

\int_{- 1}^{1} e^{x^{4}} d x

非初等積分を使用する:

\int e^{x^{a}} d x = - \frac{x Γ ( \frac{1}{a} , - x ^{a} )}{a a - x ^{a}}

= [- \frac{x Γ ( \frac{1}{4} , - x ^{4} )}{4 4 - x ^{4}}]_{- 1}^{1}

限度を計算する:

- \frac{1 \cdot Γ ( \frac{1}{4} , - 1 ^{4} )}{4 4 - 1 ^{4}} - - \frac{( - 1 ) Γ ( \frac{1}{4} , - ( - 1 ) ^{4} )}{4 4 - ( - 1 ) ^{4}}

= - \frac{1 \cdot Γ ( \frac{1}{4} , - 1 ^{4} )}{4 4 - 1 ^{4}} - - \frac{( - 1 ) Γ ( \frac{1}{4} , - ( - 1 ) ^{4} )}{4 4 - ( - 1 ) ^{4}}