deletions | additions       diff --git a/Integration summation.tex b/Integration summation.tex  index 9c6c187..a34b3ac 100644  --- a/Integration summation.tex  +++ b/Integration summation.tex 
...
Does there exist an integral that equals $\zeta(s)$...  \begin{equation}  \zeta(s)\Gamma(z)=\int_0^\infty \zeta(s)\Gamma(s)=\int_0^\infty  \frac{x^{s-1}}{e^x-1} \; dx \\ \frac{d}{dx}\frac{x^{s-1}}{e^x-1} = \frac{(e^x (s-x-1)-s+1) x^{s-2}}{(e^x-1)^2} \\  \end{equation}  Therefor by the theory \begin{equation}  -\zeta(s)\Gamma(z)=\int_0^\infty -\zeta(s)\Gamma(s)=\int_0^\infty  \frac{(e^x (s-x-1)-s+1) x^{s-1}}{(e^x-1)^2} \; dx \\ \end{equation}