integrate ln sqrt (x^2-1)

Question

integrate  ln sqrt (x^2-1)

saifoo.khan · Answer

Ops, it's ln.

anonymous · Answer

oh and i suppose if i take the derivative of that i will get 
$$\ln(\sqrt{x^2-1})$$ fat chance!

saifoo.khan · Answer

so the integration for ln = 1/x 
im not really sure. i have to check  my register for it. :/

@LagrangeSon678

anonymous · Answer

its gonna be alittle harder than that

anonymous · Answer

it looks like intergration by parts.  Is that the best way to go with this problem?

anonymous · Answer

thats seems like a good route, alhtough i'll leave the work up to you

saifoo.khan · Answer

i got it. :D

saifoo.khan · Answer

wait. i got the derivatives of ln. -_-

saifoo.khan · Answer

@LagrangeSon678 , please continue.

anonymous · Answer

$$\ln(\sqrt{x^2-1})=\frac{1}{2}\ln(x-1)+\frac{1}{2}\ln(x+1)$$ is a good start, also good is to have memorized 
$$\int \ln(x)dx=x\ln(x)-x$$ otherwise it is groundhog day all over again

anonymous · Answer

don't forget to "simplfy" using properties of the logs to start. makes life much easier. the rest you can pretty much do in your head so long as you can remember what the anti derivative of the log is. memorize it, because math teachers love to put in on tests

anonymous · Answer

thanks.  for the help