Question

What is the antiderivative of `1/(1+x^2)`?

Answer 1

`tan^-1(x)+C`

Explanation:

We want a function which, when differentiated, will yield `1/(1+x^2).`

`tan^-1(x)` fulfills this requirement, as `d/dxtan^-1(x)=1/(1+x^2).`

We also add in an arbitrary constant `C,` any constant could be part of our antiderivative, as differentiating a constant yields zero.