Question

Find the integral of 1/sqrt(x^2-9)

Answer 1

Let x = 3secβ, then dx = 3secβtanβ

∫dx/√(x²-9) = ∫[(3secβtanβ)/(3tanβ)]dβ
= ∫secβdβ
= ln |tanβ - secβ| + c
= ln |√(x² - 9)/3 - x/3| + C
= ln |√(x² - 9)/x| + C