Use a Trigonometric Substitution to Evaluate the Integral $$\int \frac { \mathrm { e } ^ { \mathrm { x } } \mathrm { dx } } { \sqrt { 1 - \mathrm { e } ^ { 2 \mathrm { x } } } }$$

question 58

Multiple Choice

Use a trigonometric substitution to evaluate the integral.
- $$\int \frac { \mathrm { e } ^ { \mathrm { x } } \mathrm { dx } } { \sqrt { 1 - \mathrm { e } ^ { 2 \mathrm { x } } } }$$

• A) \(- 2 \sqrt { 1 - \mathrm { e } ^ { 2 \mathrm { x } } } + \mathrm { C }\)
• B) \(\mathrm { e } ^ { \mathrm { x } } \sin ^ { - 1 } \left( \mathrm { e } ^ { \mathrm { x } } \right) + \mathrm { C }\)
• C) \(\sin ^ { - 1 } \left( e ^ { x } \right) + C\)
• D) \(\sec ^ { - 1 } \left( e ^ { x } \right) + C\)

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