integral from 0 to x of e^{-t^6}

解答

\int_{0}^{x} e^{- t^{6}} d t

- \frac{x Γ ( \frac{1}{6} , x ^{6} )}{6 6 x ^{6}} - (- \frac{0 \cdot Γ ( \frac{1}{6} , 0 ^{6} )}{6 6 0 ^{6}})

求解步骤

\int_{0}^{x} e^{- t^{6}} d t

这是非初等函数积分:

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

= [- \frac{t Γ ( \frac{1}{6} , t ^{6} )}{6 6 t ^{6}}]_{0}^{x}

带入上下限计算后得:

- \frac{x Γ ( \frac{1}{6} , x ^{6} )}{6 6 x ^{6}} - (- \frac{0 \cdot Γ ( \frac{1}{6} , 0 ^{6} )}{6 6 0 ^{6}})

= - \frac{x Γ ( \frac{1}{6} , x ^{6} )}{6 6 x ^{6}} - (- \frac{0 \cdot Γ ( \frac{1}{6} , 0 ^{6} )}{6 6 0 ^{6}})

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