Integrate csc2x ln(tanx) dx: Solutions & Suggestions

  • Context: Graduate 
  • Thread starter Thread starter flying2000
  • Start date Start date
  • Tags Tags
    Integration
Click For Summary

Discussion Overview

The discussion revolves around the integration of the function csc²(x) ln(tan(x)) dx, with participants exploring various methods and substitutions for solving the integral. The scope includes mathematical reasoning and problem-solving techniques related to integration.

Discussion Character

  • Mathematical reasoning, Homework-related

Main Points Raised

  • One participant expresses difficulty in integrating ln(tan(x))/sin(x)cos(x) and seeks suggestions for changing it to csc²(x) ln(tan(x)) dx.
  • Another participant suggests that the integral can be simplified by multiplying both the numerator and denominator by cos(x) and using the substitution u = tan(x), followed by integration by parts.
  • A different approach is proposed involving the substitution u = ln(tan(x)).
  • A later reply indicates that the original poster successfully solved the integral after receiving suggestions.

Areas of Agreement / Disagreement

Participants present multiple approaches to the integration problem, and while some methods are suggested, there is no explicit consensus on a single preferred method. The discussion remains open to various techniques.

Contextual Notes

Participants do not clarify the assumptions or limitations of their proposed methods, and the discussion does not resolve the effectiveness of each approach.

Who May Find This Useful

Readers interested in integration techniques, particularly those involving logarithmic and trigonometric functions, may find the discussion beneficial.

flying2000
Messages
40
Reaction score
0
integrate ln(tanx)/sinxcosx dx
I want to change to integrate csc2x ln(tanx) dx , still can't work it out.
Any suggestions?
THX
 
Physics news on Phys.org
[tex]\int \frac{\ln(\tan x)}{\sin x\cos x} dx[/tex] can be integrated very easily if u multiply both the denominator & the numerator by \cos x and make the substitution \tan x -------->u and then a simple part integration...

Daniel.
 
Or you could try the substitution u = ln(tan(x)).
 
Thanks so much. I got it!
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 22 ·
Replies
22
Views
4K
  • · Replies 4 ·
Replies
4
Views
7K
  • · Replies 19 ·
Replies
19
Views
5K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 7 ·
Replies
7
Views
31K
  • · Replies 1 ·
Replies
1
Views
2K