Solving Gamma Function Int xe^-x^3 from 0 to Infinity

[Liquidxlax]

Homework Statement

\int xe^{-x^{3}}dx

from 0 to infinity

Homework Equations

\Gamma = \int x^{p-1}e^{-x}

from 0 to infinity

The Attempt at a Solution

my problem is I'm not sure what i am supposed to do with the exponent of 3 on the e, because it seems to affect the answer. Wolfram gave me gamma(2/3)/3.

My textbook states nothing on it and i can't find anything on the net.

 

[Dick]

Sure it affects the answer. Get rid of it by substituting u=x^3 and change everything to the variable u.

 

[Liquidxlax]

Sure it affects the answer. Get rid of it by substituting u=x^3 and change everything to the variable u.

worked, thank you