I really need help with this integral problem.

Question

Integral from square root of 2 to 2 of 1/(x(sqrt(x^(2)-1)). How do I evaluate it and get the answer? Thanks.

Answer 1

Use the trig substitution x = secθ

 

Then the integral becomes

 

      ∫_{(from π/4 to π/3)}(secθtanθdθ)/[secθ√tan²θ]

 

    = ∫_{(from π/4 to π/3)} dθ = θ_{(from π/4 to π/3)} = π/3 - π/4 = π/12