Integration by Parts: Help Needed with x^2 e^x^3 dx

Click For Summary

Homework Help Overview

The problem involves integrating the function x^2 e^x^3 with respect to x. Participants are discussing the appropriate method to approach this integration, particularly focusing on the interpretation of the expression e^x^3.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to begin the integration. Some participants suggest using a u substitution based on the interpretation of e^x^3, while others clarify the notation to avoid confusion. There is a discussion about whether to use integration by parts or simply a substitution.

Discussion Status

Participants are actively exploring different interpretations of the problem and suggesting various approaches. Some guidance has been offered regarding the use of substitution rather than integration by parts, but there is no explicit consensus on the best method yet.

Contextual Notes

There is a noted ambiguity in the expression e^x^3, which could lead to different interpretations. Participants are also navigating the constraints of the forum's posting format, which may affect how they present their attempts.

bondgirl007
Messages
73
Reaction score
0

Homework Statement



Integrate x^2 e^x^3 dx


Homework Equations



I = uv - integral of u'v

The Attempt at a Solution



I don't know where to begin this question at all and have been stuck on it for the past half hour. Any help would be really appreciated. :(
 
Physics news on Phys.org
e^x^3 can mean either e^(x^3) or (e^x)^3. Use parentheses! (If not TeX). If it's the former then d(x^3)=3*x^2, suggest a u substitution.
 
Last edited:
Sorry about that. I'll try again.
 
I'm not sure how to use the tags here so I'll just post a picture.
http://img231.imageshack.us/img231/1954/52551832cl9.png
 
Last edited by a moderator:
that doesn't really help...
 
That's how it is in my textbook though.
 
Ok, we'll guess. I think it probably means e^(x^3). Can you suggest a u substitution?
 
...in which case, you don't need to "integrate by parts". you just need the substitution which was suggested.

(which bond girl are you? Ursella Andress?)
 
Here's what I have done
u = x^2
v = 3x^2 e^(x^3)
du = 2x dx
dv = e^(x^3)2x dx

I = x^2 3x^2 e^(x^3) - integral of 3x^2 e^(x^3)

I'm not sure how to integrate the 3x^2 e^(x^3).
 
  • #10
use the substitution y=x^3 and that's it. just "change variables" not "integrate by parts".
 
  • #11
I'll try that - thanks!
 

Similar threads

How Do You Correctly Apply Integration by Parts to ∫-e^(2x)*sin(e^x) dx?
  • · Replies 9 ·
Replies
9
Views
2K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
  • · Replies 7 ·
Replies
7
Views
2K
Evaluate limit of this integral using positive summability kernels
  • · Replies 2 ·
Replies
2
Views
1K
Finding the Fourier cosine series for ##f(x)=x^2##
  • · Replies 4 ·
Replies
4
Views
3K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
  • · Replies 3 ·
Replies
3
Views
2K
Integral of 1 / (x^2 + 2) dx ?
  • · Replies 54 ·
2
Replies
54
Views
16K
Integral of e^cosx: Answers Sought
  • · Replies 11 ·
Replies
11
Views
3K
Integrate (xsinx - cosx)/x^2 with Intro Calc Techniques
  • · Replies 3 ·
Replies
3
Views
2K
Prove that the integral is equal to ##\pi^2/8##
  • · Replies 105 ·
4
Replies
105
Views
11K
Integrals that keep me up at night
  • · Replies 22 ·
Replies
22
Views
3K