Answer
$\sqrt 3 \ln (\dfrac{b}{a})$
Work Step by Step
Here, we have
$ ds=\sqrt {(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2+(\dfrac{dz}{dt})^2} dt$
and $ds= \sqrt 3 dt$
This implies that
$L=\int_{a}^{b} \dfrac{t+t+t}{t^2+t^2+t^2}( \sqrt 3 dt)$
or, $\sqrt 3\int_{a}^{b} \dfrac{1}{t} dt=\sqrt 3 [\ln (b)-\ln (a)]$
Thus, the line integral $L=\sqrt 3 \ln (\dfrac{b}{a})$
