∫ 0 1 ( e z + 1 e z + z ) = ∫ ( ( e z + 1 ) ( 1 e z + z ) ) u = e z + z d u = e z + 1 {\displaystyle {\begin{aligned}\int _{0}^{1}\left({\frac {e^{z}+1}{e^{z}+z}}\right)&=\int _{}^{}\left((e^{z}+1)({\frac {1}{e^{z}+z}})\right)u=e^{z}+zdu=e^{z}+1\end{aligned}}}
