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integrate:dx/((x-1)sqrt(x^2-2)

a tutor here direct me to a page but i do not know how to use it i tried but it did not show me any step...i need help plz

1 answer

dx/((x-1)sqrt(x^2-2))

OK. First step is a trig substitution.

x = √2 sec(u)
x^2-2 = 2tan^2(u)
dx = √2 sec(u) tan(u) du

now the integral is

sec(u)/(√2 sec(u)-1) du

see what you can do with that.
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