I need to evaluate the following integral $$\int_0^\infty x^{\mu}\exp(-{\lambda}x^\kappa)\,dx$$ (where $\mu$, $\lambda$, and $\kappa$ are are all real) in terms of the Gamma function $\Gamma(t)=\int_0^\infty x^{t-1}e^{-x}\,dx$.
I am thinking that I need to make a substitution, but my previous attempts have failed, as after making the substitutions, I still have an $x$ term remaining in the integrand.
Since the parameters aren't given specific values, I am not sure how to proceed, since similar questions in which I have had to make a substitution, I have had $\mu=\kappa$.
If a substitution is required, what is it?