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

question 160

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

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