Change the integration variable `x to xdh=x/h` 

    eq = ArcTan[1/d*Sqrt[(a + b)/(1 - b)]] - (Vi/h)*Integrate[Sqrt[(1 + (xdh)^2)^(-1)], {xdh,(1/2)*Log[b], 0}] h + (Pi/4) +m*Pi

`ConturPlot` shows possible real solutions `{Vi,b}`

    ContourPlot[0 == eq, {Vi, .8, 5}, {b, 0.0, .6}, FrameLabel -> {Vi, b}]

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/6IF90.png