Posted by Vivian on Wednesday, February 8, 2012 at 1:35am.
I split (x+3)/(x^2+9) into
x/(x^2 + 9) + 3/(x^2+9)
= (1/2)(2x/(x^2+9) + 3/(x^2 + 9)
the integral of the first is (1/2) ln(x^2+9)
the second I looked up in my old integral tables and I would get
tan^2 (x/3)
so ∫[(x+3)/(x^2 +9)] dx
= (1/2)ln(x^2+9) + tan^1 (x/3)