` int _ 0 ^ 1 cot ^ ( - 1 ) ( 1 - x + x ^ 2 ) dx ` equals :

int cos [2 cot ^(-1) sqrt ((1 -x )/( 1 + x ))] dx is equal to:

int (1-cot x)cosec^(2) x dx equals :

inte^(x) ( 1- cot x + cot^(2) x) dx is eqal to

If int_0^1 f(x) dx = 1, int_0^1 xf(x) dx = a, int_0^1 x^2 f(x) dx = a^2 , then int_0^1 (a - x)^2 f(x) dx is equal to :

int_0^1cot^(- 1)(1-x+x^2)dx

int cot^(-1)(1-x+x^(2))dx