Question

How do you find the integral of `dx/(1+x^2)`?

Answer 1

`tan^-1 x +C`

Explanation:

Let `x = tan theta`, so that `dx=sec^2 theta d theta`

`int (1dx)/(1+x^2)` = `int (sec^2 theta d theta)/ sec^2 theta`

`int d theta = theta +C`

= `tan^-1 x +C`