These questions share a similar theme.

1) Integral of (x-1)dx/(x^2 - 4x + 5)

I have tried dividing this problem into two fractions, without result. I thought maybe difference of squares somehow on the bottom, x^2 - 4x + 4 + 1, but what then?

2) xdx/x^4 + x^2 + 1

I set u = x^2

du = 2x

= 1/2 Integral of du/u^2+u+1

And I STILL can't solve it! It is in a really simple form now, 1/u^2 + u + 1, what am I doing wrong?

Seems like it would be obvious, but it's evading me.

Sigh. Why is this not obvious to me? V. frustrating