Use the integral test to determine whether the series converges: $\displaystyle \sum^{\infty}_{n=1} \frac{1}{(2n+1)^3}$

I was thinking instead of using the integral test I just make $\displaystyle (2n+1) = x$ which becomes $\displaystyle \sum^{\infty}_{n=1} \frac{1}{(x)^3}$ which is a p-series and is clearly convergent. Would that be a valid assumption?