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" (8) "int(0)^(1)sin(2tan^(-1)sqrt((1+x)...

" (8) "int_(0)^(1)sin(2tan^(-1)sqrt((1+x)/(1-x)))dx=

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

int_(0)^(1) sin{2 tan^(-1)sqrt((1+x)/(1-x))}dx=

int_(0)^(1) sin{2 tan^(-1)sqrt((1+x)/(1-x))}dx=

int_0^(1) sin (2 tan^(-1) sqrt((1+x)/(1-x))) dx =

int_0^1 sin(2tan^(-)sqrt((1+x)/(1-x))) dx

The value of int_(0)^(1)sin[2tan^(-1)sqrt((1+x)/(1-x))]dx is equal to -

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