integral of e^{-x^5}

解答

\int e^{- x^{5}} d x

- \frac{x Γ ( \frac{1}{5} , x ^{5} )}{5 5 x ^{5}} + C

求解步骤

\int e^{- x^{5}} 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}{5} , x ^{5} )}{5 5 x ^{5}}

解答补常数

= - \frac{x Γ ( \frac{1}{5} , x ^{5} )}{5 5 x ^{5}} + C

\int \frac{1}{t ^{2} 16 - t ^{2}} d t

s l o p e y = 2 - x^{3}, (1, 1)

y^{^{'}} = (t + y)^{2} - 1

\int \frac{3 x ^{3} - 4 x ^{2} - 14 x + 8}{x ^{2} - 3 x + 1} d x

d er i v a t i v e f (x) = ∣ x - 9 ∣