With the given variable substitution, u=x3, we obtain
and because the integral contains x2 as a factor, we can bundle it together with dx and replace the combination with 31du,
Thus, the answer is
where C is an arbitrary constant.
x3
dx=3x2dx 
ex3x2dx=
u=x3
=eu31du=31eu+C. ex3x2dx=31ex3+C
