\(\displaystyle \displaystyle{\int \frac{sin(2x)}{1 + cos^2(x)} dx}\) ... then it should have been written as The integral of sin(2x)/ [1 + cos^2(x)] dx
If it is the above integral - please edit your post and we will have a discussion about solving it.
If the problem is \(\displaystyle \int \frac{sin(2x)}{1+ cos^2(x)} dx\) then I would be inclined to use the trig identity
\(\displaystyle sin(2x)= 2 sin(x)cos(x)\) and let \(\displaystyle u= cos(x)\) first.
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