## anonymous 4 years ago please integrate this. =) sqr (x^2 - 1)dx /x

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

Now can you do it?

5. anonymous

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

6. anonymous

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!