Evaluate the Integral by Making a Substitution and Then Using $\int \frac { e ^ { x } } { e ^ { 2 x } - 25 } d x$

question 161

Multiple Choice

Evaluate the integral by making a substitution and then using a table of integrals.
- $\int \frac { e ^ { x } } { e ^ { 2 x } - 25 } d x$

• A) \(\frac { 1 } { 10 } \ln \left| \frac { 5 - \mathrm { e } ^ { 2 \mathrm { x } } } { \mathrm { e } ^ { 2 \mathrm { x } } + 5 } \right| + \mathrm { C }\)
• B) \(\frac { 1 } { 10 } \ln \left| \frac { 5 - x } { x + 5 } \right| + C\)
• C) \(\frac { 1 } { 10 } \ln \left| \frac { 5 - \mathrm { e } ^ { \mathrm { x } } } { \mathrm { e } ^ { \mathrm { x } } + 5 } \right| + \mathrm { C }\)
• D) \(\frac { 1 } { 10 } \ln \left| \frac { \mathrm { e } ^ { \mathrm { x } } + 5 } { \mathrm { e } ^ { \mathrm { x } } - 5 } \right| + \mathrm { C }\)

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