find the following integral

Question

(1) dx/25+(x-5)^2

(2) cos^8xsinxdx

Answer 1

(1) Do you mean dx/(25+(x-5)^2) or dx(1/25+(x-5)^2)?

(2) (cos(x))^8sin(x)dx

let u = cos(x)
du = - sin(x)
= integral(-u^8du)
= -(u^9)/9 +C
= -((cos(x))^9)/9 +C