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## Main Question or Discussion Point

Check this out,

1/(x

where "a" is a constant

When this function is integrated, if a is positive then we get something like arctan of something, if a is 0 we simply get -1/x, and if a is negative then we get something involving the natural logarithm, and yet there's something very similar to all 3 graphs.

But how is it that a small change in this constant a can lead to such drastic changes in the functional form of the integral?

1/(x

^{2}+a)where "a" is a constant

When this function is integrated, if a is positive then we get something like arctan of something, if a is 0 we simply get -1/x, and if a is negative then we get something involving the natural logarithm, and yet there's something very similar to all 3 graphs.

But how is it that a small change in this constant a can lead to such drastic changes in the functional form of the integral?