$\int \sqrt { 1 + e^{x^{2}} } \, d x$\
In the integral, if the substitution $u = \sqrt { 1 + e ^ { x } }$ is made, which of the following integrals is obtained?\
A) $\int \frac { 2 u } { u ^ { 2 } + 1 } d u$\
B) $\int \frac { u ^ { 2 } } { u ^ { 2 } + 1 } d u$\
C) $\int \frac { 1 } { u ^ { 2 } - 1 } d u$\
D) $\int \frac { u } { u ^ { 2 } - 1 } d u$\
E) $\int \frac { 2 u ^ { 2 } } { u ^ { 2 } - 1 } d u$