Integrate (e^4x)/x: Step-by-Step Guide

  • Thread starter shansalman
  • Start date
  • Tags
    Integrating
In summary, integration by parts may not be helpful for the given equation and it cannot be defined by any known functions. It is believed that a new formula, similar to existing integration rules, will be discovered in the future. The Exponential Integral function has been proposed as a possible solution, but it is simply a definite integral. It is speculated that this new function could have significant applications and potentially lead to the discovery of the grand unified field theory. However, it is already known and is not an anti-derivative.
  • #1
shansalman
1
0
How would you integrate this equation?
 
Physics news on Phys.org
  • #2
You could use integration by parts. If it helps, rewrite it as:
x-1*e4x
 
  • #3
I don't think that integration by parts is going to be too helpful here. This is definitely not a standard textbook exercise in basic integration.
 
  • #4
By definition, it is -Ei(1,-4x). Where Ei is the exponential integral.

Hope this helps.

;0
 
Last edited:
  • #5
Using a substitution, this integral can be simplified to [tex] \int \frac{e^u}{u} du [/tex]
No matter how hard you try, you can never succeed in integrating this integral. It cannot be defined by any known functions, much like [tex] \int \sin(x^2) dx [/tex] and [tex] \int \frac{sinx}{x} dx [/tex].
 
Last edited:
  • #6
mlleRosie is correct. There is no current known method for integrating this type of equation.

Simply put, I am sure your familiar with the chain rule, power rule, Lhoptials rule, etc... The method to solve this is similar to those... it just hasnt been discovered yet. In theory there is a number formula (like Log, sine, tan, cos, etc) that hasnt been figured out and that will be used in the new formula. Cool huh?

Well go get yourself a nobel prize and invent the shansalman's rule for integrating this!
 
  • #7
Some others I just came up with are

Integrate: square root(1+x^3) dx

integrate: e^x^2 dx

How do you guys do that latex stuff?
 
  • #8
ssb said:
Well go get yourself a field's medal and invent the shansalman's rule for integrating this!

fixed.

I don't think they'd give a nobel prize for that, unless it had a very significant use in physics, ecomonics, chemistry, or biology.
 
  • #9
Im sure your right. It would be amazing nevertheless.

Just think, there is something that exists out there that will probably be taught at the high school level once its discovered. Its something simple yet nobody has figured it out yet. (This whole paragraph is obviously a maybe).

Just its really exciting isn't it ?!

Maybe this new function will relate some of the major theories out there (e = mc^2 and some others) and we can finally prove the grand unified field theory (the everything theory). Then I am sure it will get a nobel and maybe we could travel to the stars! OMG I am so excited now! Its like wondering "what if" if you won the lottery.
 
Last edited:
  • #10
Found another one:

Integrate sin(x^2)
 
  • #11
ssb said:
Im sure your right. It would be amazing nevertheless.

Just think, there is something that exists out there that will probably be taught at the high school level once its discovered. Its something simple yet nobody has figured it out yet. (This whole paragraph is obviously a maybe).

Just its really exciting isn't it ?!

Maybe this new function will relate some of the major theories out there (e = mc^2 and some others) and we can finally prove the grand unified field theory (the everything theory). Then I am sure it will get a nobel and maybe we could travel to the stars! OMG I am so excited now! Its like wondering "what if" if you won the lottery.

The function has been discovered already. ZioX mentions it in the third reply to this thread. It is the Exponential Integral function, one of a family of functions which has been studied by many a mathematician.
 
  • #12
EUREKA! we are all going to be rich! :-) that is too cool. I am behind in my reading it looks like!
 
  • #13
I haven't been to that page but I assure all here that the Exponential Integral Function is just a definite integral, not an anti-derivative. And that is no amazing achievement, I can do the same for any function, watch.

[tex]\int f(x) dx = F(x) + C, \frac{dF(x)}{dx} = f(x)[/tex].

Now if i wanted, I could study the properties of a particular F(x), as they did for the Exponential Integral Function.
 

FAQ: Integrate (e^4x)/x: Step-by-Step Guide

1. What is integration?

Integration is a mathematical process that involves finding the area under a curve. It is the inverse operation of differentiation, and is used to find the original function given its derivative.

2. Why is integration important?

Integration is important because it has many practical applications in fields such as physics, engineering, and economics. It allows us to find the total value or quantity of something, as well as calculate rates of change.

3. How do you integrate a function?

To integrate a function, you need to follow a set of rules and techniques. First, you need to identify the function and its limits of integration. Then, you can use various integration techniques such as substitution, integration by parts, or partial fractions to solve the integral.

4. What is the step-by-step process for integrating (e^4x)/x?

The step-by-step process for integrating (e^4x)/x involves first rewriting the function as (e^4x)*(1/x). Then, using the substitution method, let u = 4x and du = 4dx. This will give you an integral in terms of u. Next, use the power rule to integrate e^u, and then substitute back in the original variable x to get the final answer.

5. Are there any tips for solving integrals?

Yes, there are some tips that can make solving integrals easier. These include recognizing common integration patterns such as the power rule, using appropriate substitution, and being familiar with integration techniques such as integration by parts and partial fractions. It is also helpful to practice regularly and review basic algebraic concepts.

Back
Top