Integrals of Trigonometric Functions

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Homework Help Overview

The discussion revolves around three integral problems involving trigonometric functions and separation of variables. The subject area includes calculus, specifically integration techniques and differential equations.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss using a reduction formula for the first integral and suggest a substitution for the second. There is mention of separating variables for the third problem, with one participant noting a challenge with partial fraction decomposition.

Discussion Status

Some participants have offered guidance on potential methods for each problem, while others are actively attempting to apply these suggestions. There is progress noted on the first problem, but the second and third problems remain under discussion.

Contextual Notes

One participant indicates they have work on scratch paper but are experiencing difficulties, suggesting that some information may be incomplete or unclear. The nature of the homework implies constraints on providing direct solutions.

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Homework Statement



I have three problems that I'm having a hard time with. I'd appreciate any help with
any of the three problems.

[tex]\int((cos(x))^6)dx[/tex]

AND

[tex]\int(x^3 * sqrt(x^2 - 1)[/tex]

AND

Solve for y (separation of variables):
dy/dx = ((2y + 3)^2)/((4x + 5)^2)


Homework Equations



Separation of variables for 3rd problem.


The Attempt at a Solution



I have work on scartch paper but I get stuck.
 
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For the first integral, use the reduction formula for cosine.

For the second, try u = x2

For the third, did you try getting everything with y on one side and everything with x on the other?
 
thank you. I am going to try this right now. for the third i got down to an integral that would need partial fraction decomposition but got stuck. :(
 
I finally got the first one. so just the 2nd and 3rd problems now.
 

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