If we have 1/(1+x2), 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+x2). Then we say that if we replace x with tan(Θ), we can replace the denominator with its identity, sec2(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).