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

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

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if 0ltalphalt1 and I=int_(-1)^1dx/(sqrt(1-2alphax+alpha^2) then I equals

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

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

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

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

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

Let I = int_1^2 (dx)/(sqrt(1 + x^2)), J = int_1^2 (dx)/(x) , then

int_(-1)^(1)(x)/(sqrt(1-x^(2)))*sin^(-1)(2x sqrt(1-x^(2)))dx is equal to

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

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

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