Im struggling to finish this one

I = 1/( 2 + cos x) dx

using substitution t = tan1/2 x

I sub in for cos and recalcualte to give me

I = 2/(t^2 + 3) dt

I can see this is clse tot the form I = a/(t^2 + a^2) dt but can complete.

Can someone show me where I'm missing the link?

Thanks, Dan