Question

How would i go about using partial fraction decomposition on the integral, (int) (x+2)/(x^2+4x+5) dx.
Is there a way to do this utilizing complex number decomposition.

Answer 1

You don't want to dive into this with complex numbers. Partial fractions will not help here.

Let
u = x^2+4x+5
du = 2(x+2) dx
and that is
∫ 1/2 du/u = 1/2 lnu = 1/2 ln(x^2+4x+5) + C

Answer 2

Unfortunately I have to make sure that the normal computation and the complex computation match up

Answer 3

well, you can go ahead and do that, but you better make sure you understand something about the inverse hyperbolic functions, especially argtanh(x), which is defined with complex logs.