Integral test for series $\sum_{n = 18}^{\infty} \frac{n^2}{(n^3 + 3)^{7/2}}$ I am stuck on how to more so algebraically to solve this problem. I understand that you would rewrite the series as a function of x, and then evaluate the integral from 18 to infinity - but that's all I got. Any pointers? Thank you in advance. 

Use the integral test to determine whether the infinite series is convergent.
  $$\sum_{n = 18}^{\infty} \frac{n^2}{(n^3 + 3)^{7/2}}.$$


Let $$u=x^3+3$$ to evaluate the $$\int_{18}^{\infty} \frac{x^2}{(x^3 + 3)^{7/2}} dx$$ 
