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help step by step? integral of (2sec^2(x))/(1+tan^2(x))dx

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I want to be shown step by step.. explaining..
start using the identity \[1+\tan^2 x= \sec^2 x\]
ok wait.

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Other answers:

you can also do it via substitution: integral of (2sec^2(x))/(1+tan^2(x))dx = 2 (integral of (sec^2(x))/(1+tan^2(x))dx) because 2 is a constant 2 (integral of (sec^2(x))/(1+tan^2(x))dx) ; u=tan(x) du= sec(x)^2 then you're left with 2 (integral of 1/(1+u^2)dx) ; you may notice this is equal to 2arctan(u) substitute tanx back in for u, and you recieve 2arctan(tan(x)) = 2x The most general version of this is 2x+C which is your answer (sorry if the math text is a bit hard to read (I'm new here and really lost lol)

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