What is the integral of e^{-(x^2)^2}x^2)^2 ?

The integral of e^{-(x^2)^2}x^2)^2 is x^{16}e^{-x^{16}}+C

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

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

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

Solution steps

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

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

= \int e^{- x^{16}} d (((x^{2})^{2})^{2})^{2}

Integral of a constant:

\int a d x = a x

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

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

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

Add a constant to the solution

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

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What is the integral of e^{-(x^2)^2}x^2)^2 ?
The integral of e^{-(x^2)^2}x^2)^2 is x^{16}e^{-x^{16}}+C