integral from x to x^2 of e^{t^4}

解

\int_{x}^{x^{2}} e^{t^{4}} d t

- \frac{x ^{2} Γ ( \frac{1}{4} , - ( x ^{2} ) ^{4} )}{4 4 - ( x ^{2} ) ^{4}} - (- \frac{x Γ ( \frac{1}{4} , - x ^{4} )}{4 4 - x ^{4}})

解答ステップ

\int_{x}^{x^{2}} e^{t^{4}} d t

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{t Γ ( \frac{1}{4} , - t ^{4} )}{4 4 - t ^{4}}]_{x}^{x^{2}}

限度を計算する:

- \frac{x ^{2} Γ ( \frac{1}{4} , - ( x ^{2} ) ^{4} )}{4 4 - ( x ^{2} ) ^{4}} - (- \frac{x Γ ( \frac{1}{4} , - x ^{4} )}{4 4 - x ^{4}})

= - \frac{x ^{2} Γ ( \frac{1}{4} , - ( x ^{2} ) ^{4} )}{4 4 - ( x ^{2} ) ^{4}} - (- \frac{x Γ ( \frac{1}{4} , - x ^{4} )}{4 4 - x ^{4}})