What is the Integral of e to the Power of 3lnx and e to the Power of 3x?

  • Thread starter Thread starter iRaid
  • Start date Start date
  • Tags Tags
    Hard Integral
Click For Summary

Homework Help Overview

The problem involves finding the integral of the expression \(\int e^{3\ln x} + e^{3x} \, dx\), which presents two components that may require different approaches for integration.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss whether to use a substitution involving \(e\) and express uncertainty about the rules related to exponentials and logarithms. Some participants suggest simplifying \(e^{3\ln x}\) using the property that \(e^{\ln(x)} = x\).

Discussion Status

The discussion is ongoing, with participants providing insights into the properties of logarithms and exponentials. There is a recognition of the basic rules involved, but some participants express frustration and stress regarding their understanding and preparation for exams.

Contextual Notes

Participants mention feeling overwhelmed by the material and the pressure of an upcoming AP exam, which may influence their engagement with the problem.

iRaid
Messages
558
Reaction score
8

Homework Statement


\int e^{3lnx} + e^{3x} dx


Homework Equations





The Attempt at a Solution



Not sure if I should use an e substitution or if I'm forgetting some easy e rules... Any help appreciated.
 
Physics news on Phys.org
You really have two separate problems there. e^(ln(x))=x will help with one of them.
 
e^(lnx)=x, do you mean the derivative of e^lnx=x? Why do they give me some stupid rule I don't know -.-"
 
iRaid said:
e^(lnx)=x, do you mean the derivative of e^lnx=x? Why do they give me some stupid rule I don't know -.-"

No, I mean e^(ln(x))=x. e^x and ln(x) are inverse functions. You didn't know that? Use that to simplify e^(3*ln(x)).
 
It's just too much to remember. Thank you though.
 
iRaid said:
It's just too much to remember. Thank you though.

You're welcome. It is pretty basic though. It's sort of the definition of what 'ln(x)' means.
 
Yeah I should of thought more, but I kind of instantly thought it was harder than I thought, usually what I do when I see e lol. Plus kind of stressed for this stupid AP exam -.-
 
iRaid said:
Yeah I should of thought more, but I kind of instantly thought it was harder than I thought, usually what I do when I see e lol. Plus kind of stressed for this stupid AP exam -.-

Well, try and destress. That's ones not that hard if you don't panic.
 
I know I know :\
 
  • #10
iRaid said:
I know I know :\

Good luck!
 
  • #11
Thank you..
 

Similar threads

Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
  • · Replies 7 ·
Replies
7
Views
2K
How do I differentiate the function F(x)=4^{3x}+e^{2x}?
  • · Replies 5 ·
Replies
5
Views
2K
Integrating x^2e^-3lnx: Tips and Tricks for Solving Tricky Integrals
  • · Replies 3 ·
Replies
3
Views
1K
Integrating Logarithmic Functions with Binomial Terms
  • · Replies 14 ·
Replies
14
Views
3K
How should I show that all solutions are periodic?
  • · Replies 10 ·
Replies
10
Views
3K
How To Integrate 1/[sqrt (x^2 + 3x + 2)] dx?
  • · Replies 44 ·
2
Replies
44
Views
6K
How Do You Correctly Apply Integration by Parts to ∫-e^(2x)*sin(e^x) dx?
  • · Replies 9 ·
Replies
9
Views
2K
How do I integrate (e^3lnx + e^3x)dx without a calculator?
  • · Replies 4 ·
Replies
4
Views
10K
Arc length of vector function - the integral seems impossible
  • · Replies 2 ·
Replies
2
Views
2K
Unraveling an ODE: Solving a First Order Equation with Separation of Variables
  • · Replies 5 ·
Replies
5
Views
1K