$\text { Find } \int e ^ { 2 x } \sqrt { 1 - e ^ { 4 x } } d x$

question 42

Multiple Choice

$\text { Find } \int e ^ { 2 x } \sqrt { 1 - e ^ { 4 x } } d x$

• A)
• \(\int e ^ { 2 x } \sqrt { 1 - e ^ { 4 x } } d x = \frac { 1 } { 4 } \left( \arcsin \left( e ^ { 2 x } \right) + e ^ { 2 x } \sqrt { 1 - e ^ { 4 x } } \right) + C\)
• B)
• \(\int e ^ { 2 x } \sqrt { 1 - e ^ { 4 x } } d x = \left( e ^ { 2 x } - e ^ { 2 x } \sqrt { 1 - e ^ { 4 x } } \right) + C\)
• C)
• \(\int e ^ { 2 x } \sqrt { 1 - e ^ { 4 x } } d x = \left( \arcsin \left( e ^ { 2 x } \right) - e ^ { 2 x } \sqrt { 1 - e ^ { 4 x } } \right) + C\)
• D)
• \(\int e ^ { 2 x } \sqrt { 1 - e ^ { 4 x } } d x = \frac { 1 } { 4 } \left( \arccos \left( e ^ { 2 x } \right) + e ^ { 2 x } \sqrt { 1 - e ^ { 2 x } } \right) + C\)
• E)
• \(\int e ^ { 2 x } \sqrt { 1 - e ^ { 4 x } } d x = \frac { 1 } { 4 } \left( e ^ { 2 x } + e ^ { 2 x } \sqrt { 1 - e ^ { 2 x } } \right) + C\)

---

Definitions:

Price Rise

An increase in the monetary value of goods or services over time.

Original Bundle

Describes a combination of goods and/or services that an individual initially chooses based on their preferences and income constraints.

Price Rise

An increase in the cost of goods or services, often reflecting factors like inflation, increased production costs, or higher demand.

Units of Y

Quantitative measures of a variable Y, often used in economics to denote quantity or amount.