I've tried to integrate by part, but it seems that Mathematica is still not able to integrate.
Integrate[(24(1-z)^a)/((-1+(1-z)^a)^2z)+(24a(1-z)^(3a) Hypergeometric2F1[1, 1, 2 - a, 1/z])/((-1+a)(-1+(1-z)^a)^3 (-1+z)z)-(24 a Hypergeometric2F1[1, 1,2+a,1/z])/((1+a)(-1+(1-z)^a)^3 (-1+z)z),z]
We actually know the result exists but we want to get it from this integral.
Is there any commands in Mathematica that are usually helpful in doing integral?
Assumptions
toIntegrate
. For instance the range ofa
, or whether it is real and the like. By default, Mathematica assumes the most general scenario which is often not necessary, so that assumptions help to find a (simpler) solution $\endgroup$ – Lukas May 31 '16 at 20:52a
e.g.-1/2, 1/2, 3/2
. Fora
integer it isComplexInfinity
. What are assumptions ona
? $\endgroup$ – Artes May 31 '16 at 21:08Integrate[(24 (1 - z)^a)/((-1 + (1 - z)^a)^2 z), z, Assumptions -> 0 < a < 1]
returns unevaluated, so it is not surprising that the full integral does as well. In fact, this simpler integral returns an answer only fora
a rational number, and even then typically in terms ofRootSum
. The only instance of a solution to the full integral that I found was a -> 1/2. $\endgroup$ – bbgodfrey Jun 1 '16 at 4:27