05 Mar '16 19:2810 edits

This one has really got me totally stumped:

what is the integral of:

∫[θ = 0, ∞] ( h (θ^m) ) / ( e^( θ(h + s) ) ) dθ

m ∈ ℕ,

m>0,

h, s, m, θ ∈ ℝ,

s, m, θ ≥ 0,

h>0

( so all positive i.e. none are allowed to be negative )

and why?

I tried Wolfram-Alpha this but it wouldn't give me the answer directly and what I seemed to indirectly infer from Wolfram-Alpha (by inputting a series of reduced versions of the above integral into it ) is that it

h θ^( (m-1)! ) / ( ( h + s )^m )

(bear in mind that m∈ℕ and m>0 else cannot have that factorial )

BUT it seems to me that this MUST be false because I just get complete nonsense when I test that with a computer program.

what is the integral of:

∫[θ = 0, ∞] ( h (θ^m) ) / ( e^( θ(h + s) ) ) dθ

m ∈ ℕ,

m>0,

h, s, m, θ ∈ ℝ,

s, m, θ ≥ 0,

h>0

( so all positive i.e. none are allowed to be negative )

and why?

I tried Wolfram-Alpha this but it wouldn't give me the answer directly and what I seemed to indirectly infer from Wolfram-Alpha (by inputting a series of reduced versions of the above integral into it ) is that it

*implies*it is:h θ^( (m-1)! ) / ( ( h + s )^m )

(bear in mind that m∈ℕ and m>0 else cannot have that factorial )

BUT it seems to me that this MUST be false because I just get complete nonsense when I test that with a computer program.