24/05/07 18:00:43.13 OgbPgxVI.net
>>936
nを実数として
(∂/∂n) x^n = (∂/∂n) e^{n･log(x)}
= e^{n･log(x)}・log(x)
= (x^n) log(x),
I[n] = ∫[1,e] (∂/∂n) x^n dx
= (d/dn)∫[1,e] x^n dx
= (d/dn) [ x^{n+1} /(n+1) ](x：1→e)
= (d/dn) (e^{n+1}－1)/(n+1)
= (n･x^{n+1}－1)/(n+1)^2,