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

[NCyellow]

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...

 

[Dick]

What's the derivative of e^(e^(4x))?

 

[NCyellow]

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.

 

[Dick]

Use the chain rule. Don't guess.

 

[NCyellow]

With chain rule, is it 4(e^4)?

 

[Dick]

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

 

[NCyellow]

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?

 

[Dick]

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