Question

please integrate this. =)

sqr (x^2 - 1)dx /x

Answer 1

\[\int\limits \sqrt{x^2 - 1} dx / x\]

Answer 2

Put x^2 -1 = t^2
2xdx=2tdt
dx=tdt/x
it becomes integral of t/(t^2+1)

Answer 3

Oh sorry it becomes t^2/(t^2+1)

Answer 4

Now can you do it?

Answer 5

yeah, i'll try my best. i'll do it first. :D

Answer 6

Try : sqrt(x^2-1)/x substitute x = sec(u) and dx = tan(u) sec(u) du. Then sqrt(x^2-1) = sqrt(sec^2(u)-1) = tan(u) and u = sec^(-1)(x)
And now your integrand becomes tan^2(u) du which is nothing but tan(u)-u+constant.Now just put u = sec^(-1)(x) back to get : I = sqrt(x^2-1)-sec^(-1)(x)+constant
And if you put some restrictions on x you get : sqrt(x^2-1)+tan^(-1)(1/sqrt(x^2-1))+constant.
And you are done!