What is the integral of e^{-(x^3)^3}x^3)^3 ?

The integral of e^{-(x^3)^3}x^3)^3 is x^{81}e^{-x^{81}}+C

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integral of e^{-(x^3)^3}x^3)^3

\int e^{- (((x^{3})^{3})^{3})^{3}} d (((x^{3})^{3})^{3})^{3}

x^{81} e^{- x^{81}} + C

Solution steps

\int e^{- (((x^{3})^{3})^{3})^{3}} d (((x^{3})^{3})^{3})^{3}

(((x^{3})^{3})^{3})^{3} = x^{81}

= \int e^{- x^{81}} d (((x^{3})^{3})^{3})^{3}

Integral of a constant:

\int a d x = a x

= e^{- x^{81}} (((x^{3})^{3})^{3})^{3}

(((x^{3})^{3})^{3})^{3} = x^{81}

= x^{81} e^{- x^{81}}

Add a constant to the solution

= x^{81} e^{- x^{81}} + C

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What is the integral of e^{-(x^3)^3}x^3)^3 ?
The integral of e^{-(x^3)^3}x^3)^3 is x^{81}e^{-x^{81}}+C