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>So in Infinity there is not problem, whereas in zero, it must be c !=-1.

I mean if c=-1 there is a non-integrable singularity at x=0.

In[202]:=
f[x, a, -1] + O[x]^6
Out[202]=
SeriesData[x, 0, {1/(2*a), 0, -1/(4*a^2), 0, 1/(8*a^3), 0, -1/
(16*a^4)}, -2, 6, 1]

In[201]:=
Integrate[f[x, a, -1], {x, 0, Infinity}]
Integrate::idiv: Integral of 1/(2*a*x^2 + x^4) does not converge on \
{0,Infinity}.
Out[201]=
Integrate[1/(2*a*x^2 + x^4), {x, 0, Infinity}]

Dimitris



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