$=\int_{0}^{+\infty}\frac{2dt}{\sqrt{(t^2+\frac{3}{2})^2-\frac{1}{4}}}=\lim_{r\to+\infty} 2ln|t^2+\frac{3}{2}+\sqrt{(t^2+\frac{3}{2})-\frac{1}{4}}|\left|\right._{0}^{r}=+\infty$