If we have 1/(1+x(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}), the antiderivative for it is tan^{-1}(Θ), correct?

I'm trying to understand how the substitution needed to get this works. First we have 1/(1+x^{2}). Then we say that if we replace x with tan(Θ), we can replace the denominator with its identity, sec^{2}(Θ), correct? Is it the change of variable that allows use to make this substitution?

For some reason I'm not convinced that something isn't lost when we change x to tan(Θ).

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# Understanding the integral of 1/(1+x^2)

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