Integrating Complexity: Indefinite Integral of e^(4x+(e^4x))

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Homework Help Overview

The problem involves finding the indefinite integral of the expression e^(4x + e^(4x)), which presents challenges due to its complexity and the nature of the functions involved.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the potential use of integration by parts and consider splitting the expression into two parts. There are attempts to apply substitution methods, though some participants express confusion regarding the effectiveness of these approaches. Questions about the derivative of e^(e^(4x)) arise, leading to discussions about the chain rule and its application.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the application of calculus rules. Some guidance on the chain rule has been provided, but there is no explicit consensus on the best approach to take.

Contextual Notes

Participants note difficulties with the complexity of the integral and express uncertainty about the application of derivatives and integration techniques. There is an emphasis on reviewing foundational concepts, such as the chain rule, as part of the discussion.

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Homework Statement



Indefinite integral:
e^(4x+(e^4x))


Homework Equations



I'm thinking integration by parts, involving UV minus integral of Vdu

The Attempt at a Solution


So I saw that this can be split into two: e^(4x) times e^(e^4x)).
The latter is a bit complicated. I searched on google but couldn't find anything useful. Substitution U for 4x or e^4x doesn't seem to work...
 
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What's the derivative of e^(e^(4x))?
 


umm... I'm going to take a guess and say e^4 or e^e^4? But how is it done? I am a bit confused on it.
 


Use the chain rule. Don't guess.
 


With chain rule, is it 4(e^4)?
 


Where did the x go? I think you should review the chain rule before you answer again.
 


well, derivative of e^4x is 4e^4x. So that must be an element of the entire answer.
So it will be (something)(4e^4x). But how do you go about deriving the first run?
 


Use parentheses to group things, ok? The derivative of f(g(x)) is f'(g(x))*g'(x). What are f and g?
 

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