Integrals of Trigonometric Functions

[recon_ind]

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.

$$\int((cos(x))^6)dx$$

AND

$$\int(x^3 * sqrt(x^2 - 1)$$

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.

 

[Bohrok]

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?

 

[recon_ind]

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. :(

 

[recon_ind]

I finally got the first one. so just the 2nd and 3rd problems now.