Integration By Parts?

Question

integral of (x+1)(2x^2+1)/(x^4+x^2)

requires integration by parts

i meant partial frctions

wow i cant spell

Answer 1

In my view the best way to do this is by "partial fraction decomposition", and I can't really see how to do it by parts.

The expression is equal to
1/x + 1/(x^2) + x/(x^2 + 1) + 1/(x^2 + 1)

(? you know how to do this?)

and then you get the primitives of those four fractions -- two logs, an inverse tan, and a power. Forget parts!

Answer 2

I would say partial fractions is probably the first thing to do.