convergence of $\int_1^{\infty}\frac{lnx}{\sqrt[3]x(x+1)}$ I need help checking if the integral:
$$\int_1^{\infty}\frac{\ln x}{\sqrt[3]x(x+1)}$$
converge or diverge.
I tried comparing to bigger integrals using $\ln x \lt x$ or making the denominator smaller but without success.
any suggestions? 

Hint: Compare it to $$\frac{\ln x}{x^{4/3}}.$$
This, incidentally, can be compared to some multiple of$$\frac{\ln(x^{1/1000})}{x^{4/3}},$$which can then be compared to$$\frac1{x^{4/3-1/1000}};$$note that the exponent in the denominator is strictly greater than $1$.
