Question

What is the integral of `1/(9+x^2)`?

Answer 1

The result should be: `1/3arctan(x/3)+C`

I can take the `9` outside the brackets and solve:

`int1/(9+x^2)dx=int1/(9*(1+x^2/9))dx=`
`=int1/3*1/(1+(x/3)^2)dx/3=`

[Remember that `int1/(1+x^2)dx=arctan(x)+C`]

`=1/3arctan(x/3)+C`

You can check the result deriving it.