that looks like the right step. I would suggest two different strategies for each term in the integral then. The first one looks like a u-substitution. The second looks like one of those gross inverse trig function anti-derivatives, see if you can look them up.
I think it should be 1/2 ln(x^2 + 4) - arctan(x/2). Take a look at the second integral; when you factor out the 4 in the denominator it will cancel with the 4 in the numerator so it should not be -2arctan(x/2) but just -arctan(x/2).
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