Convergence of an integral $\int\_1^{+\infty} \frac{1}{x\sqrt[3]{x^2+1}}\mathrm dx$

$\int\_1^{+\infty} \frac{1}{x\sqrt[3]{x^2+1}}\mathrm dx=\lim\limits\_{t\to\infty}\int\_1^{t} \frac{1}{x\sqrt[3]{x^2+1}}\mathrm dx$

Partial integration can't solve the integral $\int \frac{1}{x\sqrt[3]{x^2+1}}\mathrm dx$.

What substitution (or other methods) would you suggest?