Integrate 3/(Sqrt x^2-16) dx
I = ∫ 3/√(x^2-16) dx
= 3∫ 1/√(x^2-4^2) dx
Substitute x=4secθ
x²-4²
=4²(sec²θ-1)
=4²tan²θ
or
1/√(x²-4²)
=1/(4tanθ)
and
dx=4sec(θ)tan(θ)dθ
I = 3 ∫sec(θ)tan(θ)/tan(θ)dθ
= 3∫sec(θ)dθ
= 3ln|sec(θ)+tan(θ)| + C
Check my work.
= 3 ∫cos(
