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" Prove that "int(0)^(1/2)(dx)/((1-2x^(2...

" Prove that "int_(0)^(1/2)(dx)/((1-2x^(2))sqrt(1-x^(2)))=(1)/(2)log(2+sqrt(3))

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

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

Show that int_(0)^(1//2) (dx)/((1-2x^(2))sqrt(1-x^(2))) = (1)/(2) log(2+sqrt(3))

Prove that : int_(0)^(1) (log x)/(sqrt(1-x^(2)))dx=-(pi)/(2)log 2

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

int_(0)^((1)/(2))(xsin^(-1)x)/(sqrt(1-x^(2)))dx=(1)/(2)(1-(pi)/(2sqrt(3)))

Prove that, int_(2)^(3)(sqrt(x)dx)/(sqrt(x)+sqrt(5-x))=(1)/(2)

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