Re: Mathematica - integral exist?

i)a=b=1 : Integral=Integrate[1/Sqrt[1-Cos[x]],x]=...=
2*(-Log[Cos[x/4]] + Log[Sin[x/4]])*Sin[x/2] / Sqrt[1 -
Cos[x]]

ii)a, b=0: Integral=Integrate[1/(a*Sin[x])^3,x]=...=
(-Csc[x/2]^2/8 - Log[Cos[x/2]]/2 +Log[Sin[x/2]]/2
+Sec[x/8]^2 /8) / a^3

iii)b, a=0: Integral=...=Integrate[1/0] --> doesnt exist f(x) so that
D[Integral,x]=f[x]

**Numerical integration could be also a solution for known a,b.(using
Mathematica,or any classical progr. languages]

Summing up, an analytic solution will be always (?) welcome, but if
you're a science major or something like that, you're only going to
need a result --> a number. So, numerical methods,
don't seem so... bad after all, even if they remain a bit... 'ugly'
(for anyone used to analytic methods).

Keep up, and thanks for the challenge:$

mike lL.

.