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

question 51

Multiple Choice

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

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

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Definitions:

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The complex structure in the lower part of the torso, comprised of several bones including the sacrum and coccyx which support the spinal column and hips.

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The current geological epoch, starting approximately 11,700 years ago, following the last major ice age and characterized by the development of human civilizations.