I know from Discussing the Integral of exp(−xn) that ∫∞0e−xndx=Γ(1+1/n),n>0.
But how to evaluate ∫∞0e−(xn−x)dx,n>0?
The only substitution i found is Letx=lnu,thenex=u,anddx=1udu. Then ∫∞0e−(xn−x)dx=∫∞1e−(lnu)ndu But after this, I am stuck.
Thank you!
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