integral of e^{\sqrt[3]{x}}

解答

\int e^{3 x} d x

- \frac{x Γ ( \frac{1}{\frac{1}{3}} , - x ^{\frac{1}{3}} )}{\frac{1}{3} \frac{1}{3} - x ^{\frac{1}{3}}} + C

求解步骤

\int e^{3 x} 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}{\frac{1}{3}} , - x ^{\frac{1}{3}} )}{\frac{1}{3} \frac{1}{3} - x ^{\frac{1}{3}}}

解答补常数

= - \frac{x Γ ( \frac{1}{\frac{1}{3}} , - x ^{\frac{1}{3}} )}{\frac{1}{3} \frac{1}{3} - x ^{\frac{1}{3}}} + C

\int_{0}^{5} 1 + x^{2} d x

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