Question

How do you integrate `int4/(x^2 + 9)dx`?

Answer 1

`4/3arctan(x/3)+C`

Explanation:

Let `x=3t`, then:
`dx=3dt,`
`int4/(x^2+9)dx=int4/(9t^2+9)3dt=int4/9(t^2+1)3dt=`
`=4/3intdt/(t^2+1)=4/3arctant+C=4/3arctan(x/3)+C`