\[v(t)=\frac { \ln(1+t) }{ \sqrt { t } +t\sqrt { t } } \]

A small particle moves with a velocity as a function of time \(t\) as described above.

If the particle began its motion from the origin, at time \(t=0\). Find the exact displacement (in units) of the particle after infinitely long time.

Give your answer to 3 decimal places.

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