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

Evaluate the following : int_(0)^(1)(dx)/(x+sqrt(1-x^(2))).

If the value of the integral I=int_(0)^(1)(dx)/(x+sqrt(1-x^(2))) is equal to (pi)/(k) , then the value of k is equal to

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

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

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

If l=int_(0)^(1//2)(dx)/(sqrt(1-x^(2n))), n in N then (Where, [.] denotes G.I.F)

Prove that ln 2 lt int_(0)^(1)(dx)/(sqrt(1+x^(4))) lt (pi)/2)

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

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

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