Integrals of Trigonometric Functions

[recon_ind]

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)

THANKS soo much.

[lurflurf]

first one reduction formuls or integration by parts (integrate cos(x) differentiate cos(x)^5)
second one substitute x^2-1->w
third one just separate and integrate