Question

How do you integrate `(1/(25 + x^2) ) dx`?

Answer 1

We can rewrite this as

`int(1/(5^2+x^2))dx`

By definition, we know that the integration of the inverse of a sum of squares results in a trigonometric function as follows:

`int(1/(u^2+a^2))du=(1/a)arctan(u/a)+c`

Applying this formula to your function, we have this:

`int(1/(5^2+x^2))dx=color(green)((arctan(x/5))/5+c)`