integral of e^{x^{13}}

解答

\int e^{x^{13}} d x

- \frac{x Γ ( \frac{1}{13} , - x ^{13} )}{13 13 - x ^{13}} + C

求解步骤

\int e^{x^{13}} d x

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{x Γ ( \frac{1}{13} , - x ^{13} )}{13 13 - x ^{13}}

解答补常数

= - \frac{x Γ ( \frac{1}{13} , - x ^{13} )}{13 13 - x ^{13}} + C

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