Answer
$k[\dfrac{1}{2}-\dfrac{1}{\sqrt{30}}]$
Work Step by Step
The work done is given by
$W=\int_C F\cdot dr=\int_0^{1} \dfrac{k}{(4+26t^2)^{3/2}}\lt 2,t,5t \gt \cdot \lt 0, 1,5 \gt dt=\int_0^{1} \dfrac{k(t+25t)}{(4+26t^2)^{3/2}}dt=(\dfrac{1}{2}) \int_0^{1} \dfrac{k(52t)}{(4+26t^2)^{3/2}}dt$
Suppose $4+26 t^2=a ; 52 t dt =da$
$W=(k/2) \int_4^{30} \dfrac{dp}{p^{3/2}}=[\dfrac{k}{2}]\dfrac{-2}{p^{1/2}}]_4^{30}$
Work done, $W=[\dfrac{k}{2}]\dfrac{-2}{p^{1/2}}]_4^{30}=k[\dfrac{1}{2}-\dfrac{1}{\sqrt{30}}]$
