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) \(\sec ^ { - 1 } \left( e ^ { x } \right) + C\)

---

Definitions:

Japan's Reconstruction

The period following World War II in which Japan underwent significant political, economic, and social transformation, led by both Japanese leaders and the Allied occupation.

Second World War

A global conflict that lasted from 1939 to 1945, involving most of the world's nations and marked by significant battles across Europe, Africa, Asia, and the Pacific.

United States

A country in North America founded on July 4, 1776, known for its federal system of government and its role as a leading global economic and military power.

Eisenhower Administration

The presidency of Dwight D. Eisenhower, the 34th President of the United States, which lasted from 1953 to 1961, notable for its moderate conservative domestic and foreign policies.