What is the integral of dx/((x^2)sqrt(x^2-1))?

Question

i need th proof for it. and make sure u know that all that stuff is on the bottom and only dx is in the numerator

Answer 1

This one cries out for a
x = (cosh u) substitution. [Edit]

Simplify the integrand, and remember to replace dx
by (sinh u) du.

You will end up with a recognisable hyperbolic function problem.

The resulting integral is nearly a standard result, which you can translate back to get a function of x. [Edit]

Answer 2

Integrals containing sqrt(x^2 - a^2) you need to substitute x = a sec u to get rid of the radical in the denominator. In this case a = 1. dx = sec u tan u du

∫sec u tan u / (sec u)^2 sqrt((sec u)^2 - 1) du
∫sec u tan u / (sec u)^2 tan u du
∫1 / sec u du
∫cos u du

sin u + C

Answer 3

The integral is Sqrt(x^2 - 1)/x

Proof:

Differentiate it. You'll get your original expression.