A square frame of length \(l=1\) m, mass \(m= 1\) g, resistance \(R=1 \Omega\) is projected from a large distance towards a fixed infinitely long wire carrying current \(I= 1\) kAmp with a speed \(v_{0} = 10\) m/s.

Let \(a\) be the total distance of the left part of frame from wire in metres when the frame comes to rest.

Find \[\displaystyle \int_{a}^{\infty} \dfrac{dx}{(x(1+x))^2}\]

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