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

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits \sqrt{x^2  1} dx / x\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Put x^2 1 = t^2 2xdx=2tdt dx=tdt/x it becomes integral of t/(t^2+1)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Oh sorry it becomes t^2/(t^2+1)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah, i'll try my best. i'll do it first. :D

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Try : sqrt(x^21)/x substitute x = sec(u) and dx = tan(u) sec(u) du. Then sqrt(x^21) = 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^21)sec^(1)(x)+constant And if you put some restrictions on x you get : sqrt(x^21)+tan^(1)(1/sqrt(x^21))+constant. And you are done!
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