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

Question

1639 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-24T22:56:25

$tan^-1(x)+C$

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.

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