integral of e^{-((x^2)^2)^2}x^2)^2

解答

\int e^{- ((((x^{2})^{2})^{2})^{2})^{2}} d (((x^{2})^{2})^{2})^{2}

x^{16} e^{- x^{32}} + C

求解步骤

\int e^{- ((((x^{2})^{2})^{2})^{2})^{2}} d (((x^{2})^{2})^{2})^{2}

((((x^{2})^{2})^{2})^{2})^{2} = x^{32}

= \int e^{- x^{32}} d (((x^{2})^{2})^{2})^{2}

常数积分:

\int a d x = a x

= e^{- x^{32}} (((x^{2})^{2})^{2})^{2}

(((x^{2})^{2})^{2})^{2} = x^{16}

= x^{16} e^{- x^{32}}

解答补常数

= x^{16} e^{- x^{32}} + C

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