`int_(1)^(2)(dx)/((x+1)sqrt(x^(2)-1))`

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

int_(0)^(1)(dx)/(x sqrt(x^(2)-1)) =

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

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

int_(0)^(1)(dx)/((x+sqrt(x^(2)+1))^(3))=

int_(0)^(1)(dx)/(sqrt(x^(2)-x+1))

int_(0)^(1)(dx)/(sqrt(x^(2)-x+1))

int_(1)^(2) (x)/(sqrt(1+2x^(2)))dx

int_(0)^(1/sqrt2)(dx)/(sqrt(1-x^(2)))

Evaluate :int(dx)/(sqrt((x-1)(2-x))) by the substitution x=1+sin^(2)theta .Hence,find the value of int_(1)^(2)(dx)/(sqrt((x-1)(2-x)))