Determine the Integral by Making an Appropriate Substitution $\int \frac { \mathrm { e } ^ { \mathrm { x } } } { 1 + 2 \mathrm { e } ^ { \mathrm { x } } } \mathrm { dx }$

Multiple Choice

Determine the integral by making an appropriate substitution.
- $\int \frac { \mathrm { e } ^ { \mathrm { x } } } { 1 + 2 \mathrm { e } ^ { \mathrm { x } } } \mathrm { dx }$

A) $\mathrm { e } ^ { 2 x }$ + C
B) $\left( 1 + 2 e ^ { x } \right) ^ { 2 }$ + C
C) ln $\left| 1 + 2 \mathrm { e } ^ { x } \right|$ + C
D) $\frac { 1 } { 2 }$ ln $\left| 1 + 2 \mathrm { e } ^ { x } \right|$ + C
E) none of these