I'm a math geek... sorry :)

Have you ever gotten obsessed with some problem or activity so intensely that you continue to return to it throughout your life even though you'll probably never figure it out or master it?

I'm stuck on these two math problems that have bugged me since high school. I used to sit in my college classes and work on the problems to pass the time (Some might say they contributed to my poor college grades but I would suggest that it was the boring classes in the first placed that caused my mind to wander...) Nevertheless, I've been obsessed with two problems for some 8 or 9 years now and have made very little progress on them...

here they are if anyone has any input
x^3+Ax^2+Bx+C = 0 can be rewritten as either:
(x + u)(x + v)(x + w) = 0 where the following are true:
u + v + w = A
uv + uw + vw = B
uvw = C
alternatively it can be rewritten like this
(x + g)(x + h + i)(x + h - i) = 0
g + 2h = A
2gh + h^2 - i^2 = B
gh^2 - gi^2 = C

I can actually get pretty far with the equation but I hit a dead end... What I really need is a "trick" (like completing the square in a binomial). But there is no such thing as "Completing the Cube". And before anyone suggests solving by radicals, I've looked at that and find the solution decidedly inelegant.

The other problem is the integral of the function sin x arcsin x = y
If you graph the function it looks deceptively like a semi-circle. In fact it's very close and identical (to 10+ digits) from about -pi/8 through pi/8 but then it diverges... It came up by accident in my high school math class and while it appears like it could be solvable the integrals become ridiculously complicated after you use parts a couple times... I'm sure there is a solution but it may not be algebraicly possible (one of my great mathmatical disillusionments was in discovering that some functions just don't have integrals that can be written because our language for math is so crappy... ah well).

I'm sure that was a frightening display of geekdom for some of you, and I apologize, but blogs are supposed to be about sharing your interests and obsessions and these are shaping up to be lifelong obsessions for me :(