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