Find the Most General Antiderivative of the Function $f ( x ) = \frac { 2 e ^ { x } e ^ { 2 x } } { e ^ { x } }$

question 272

Multiple Choice

Find the most general antiderivative of the function $f ( x ) = \frac { 2 e ^ { x } e ^ { 2 x } } { e ^ { x } }$ .

• A) \(2 x + e ^ { x } + C\)
• B) \(2 x - e ^ { x } + C\)
• C) \(2 - e ^ { x } + C\)
• D) \(\frac { 2 e ^ { x } - e ^ { 2 x } } { e ^ { x } } + C\)
• E) \(2 x - 2 e ^ { x } + C\)
• F) \(\frac { 2 e ^ { x } - \frac { 1 } { 2 } e ^ { 2 x } } { e ^ { x } } + C\)
• G) \(2 + x e ^ { x - 1 } + C\)
• H) \(2 x + \frac { 1 } { 1 + x } e ^ { x + 1 } + C\)

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Definitions:

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A memorization method that involves thinking about the meaning of the term to be remembered, rather than merely repeating the word itself.

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Unusually vivid and detailed mental images that can be recalled with high precision, often referred to as “photographic memory.”

Episodic Memory

The type of memory that deals with personal experiences and specific events, including the contexts, emotions, and other associations with those events.

Semantic Memory

Long-lasting memory type focused on remembering words, concepts, or numbers, necessary for language employment and comprehension.