I got up until
But can't figure a way to take tan(x) away from cos^2(x)
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Substitution: u = tan(x) so that x = atan(u).
This gives: f'(u) = cos^2(atan(u)) = 1/(u^2 + 1)
It is now a little confusing to substitute back to 'x' (without the tangent), but we'll just have to get past that.
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