Mastering Trig Subs: Simplify \int\cos^5(x)dx without the Headache

  • Thread starter Thread starter silverdiesel
  • Start date Start date
  • Tags Tags
    Trig
Click For Summary

Homework Help Overview

The discussion revolves around simplifying the integral of \(\int \cos^5(x) \, dx\) using trigonometric substitutions. Participants are exploring strategies related to trigonometric identities and integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss factoring out terms from the integral, particularly focusing on the odd power of cosine and its implications for substitution. There are hints at using identities involving sine and cosine to facilitate the integration process.

Discussion Status

Some participants have offered insights into factoring techniques and substitutions, while others express their ongoing struggle with the topic. There appears to be a collaborative effort to clarify the approach without reaching a definitive conclusion.

Contextual Notes

Participants are navigating the complexities of trigonometric integrals, with specific attention to the handling of odd powers and the application of substitution methods. There may be varying levels of familiarity with these concepts among contributors.

silverdiesel
Messages
64
Reaction score
0
These trig subs are killing me.

[tex]\int\cos^5(x)dx[/tex]hints?
 
Physics news on Phys.org
[tex]\cos^{5} x = \left(1 - \sin^2 x \right)^{2} \cos x[/tex]

Regards,
George
 
Thanks George... I am slowly getting the hang of this. I appreciate your help.
 
One of the first things you should have learned: if you have sine or cosine to an odd power, factor out one of them to use with the dx.

cos5 x dx= (cos4 x)(cos x dx)
= (cos2 x)2 (cos x dx)= (1- sin2 x)2(cos x dx)

Now, let u= sin x.
 

Similar threads

Trouble seeing the difference between autograder answer and my own
  • · Replies 2 ·
Replies
2
Views
2K
Integrals that keep me up at night
  • · Replies 22 ·
Replies
22
Views
3K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
  • · Replies 3 ·
Replies
3
Views
2K
U-Substitution in trig integral
  • · Replies 3 ·
Replies
3
Views
3K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
  • · Replies 7 ·
Replies
7
Views
2K
Integration with Trig Sub: Simplifying the Square Root
  • · Replies 4 ·
Replies
4
Views
2K
Integrate: ## \int \cos^m(x)\sin^n(x)~dx ##
  • · Replies 11 ·
Replies
11
Views
2K
Integration using inverse trig indentities?
  • · Replies 3 ·
Replies
3
Views
1K
Integral using substitution x = -u
  • · Replies 12 ·
Replies
12
Views
2K
Differentiate ##f(x)=x\cos{x}+2\tan{x}: D/dx ##\tiny{2.4.2}##
  • · Replies 10 ·
Replies
10
Views
2K