Wednesday, December 12, 2018

definite integrals - Evaluating intinfty0e(xn+x),mathrmdx,quadn>0

I know from Discussing the Integral of exp(xn) that 0exndx=Γ(1+1/n),n>0.


But how to evaluate 0e(xnx)dx,n>0?


The only substitution i found is Letx=lnu,thenex=u,anddx=1udu. Then 0e(xnx)dx=1e(lnu)ndu But after this, I am stuck.



Thank you!

No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f:AB and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...