Trig integration question

So the question is:
∫ 1/(1+4x^2) dx with limits -1/2 to 0 (I don't know how to notate that on here) using the substitution x=1/2(tanθ)
which I worked out (after changing the limits, substituting and simplifying) as:
1/2 ∫ (1+(tanθ)^2)/(1+2(tanθ)^2) dθ with new limits -π/2 to 0.
I have no idea what to do next. Help?

No,
It is 1/2 ∫ (1+(tanθ)^2)/(1+(tanθ)^2) dθ = 1/2 ∫ dθ, with new limits -π/2 to 0

I agreed that we use x=1/2(tanθ)

Then, we get 1/2 ∫sec^2(θ)/secθ dθ = 1/2∫secθ dθ = 1/2 ln|secθ + tan θ|

Then evaluate

* I think you messed up the dx to dθ part

*Sorry, VNX was right, I took sqrt of sec^2(theta) for some reason.