find the following integral

Question

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

yes this.

Answer 1

The integral(u' / (a^2 - u^2)) = 1/a(atan(u/a)) +C

let u = x-5
du = dx

and let a = 5

So the answer is 1/5 (atan((x-5)/5)) +C

Note: atan = arctangent