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

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

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

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

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

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

int_(1)^(2)(dx)/((x-1)sqrt((x^(2)-2x)))= area of a circle then radiums of the circle is

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

The value of int_(1)^(2)(dx)/((x+1)sqrt(x^(2)-1)) is

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

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

int_(-1)^(1)(x+2)/(sqrt(x+4))dx