`int 1/ sqrt ( a^2 - x^2) = sin^-1 (x/a) + c`

int(1)/(sqrt(a^2-x^2))dx = sin^-1(x/a)+C

int(dx)/(sqrt(a^(2)-x^(2)))=sin^(-1)(x/a)+C

If int sqrt(a^(2)-x^(2))dx=(x)/(2)sqrt(a^(2)-x^(2))+k sin^(-1)(x/a)+c , then the value of k is-

int sqrt(1-sin 2x) dx

int sqrt((1-x)/(1+x))dx is equal to a) sin^(-1)x + sqrt(1 - x^(2)) + C b) sin^(-1) x - 2 sqrt(1 - x^(2)) + C c) 2 sin^(-1) x - sqrt(1 - x^(2)) + C d) sin^(-1)x - sqrt(1 - x^(2)) + C

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

int(1)/((sqrt(1-x^(2)))sin^(-1)x)dx

int(2sin^-1x)/sqrt(1-x^2)dx =

int (sin^-1x)/sqrt(1-x^2) dx.

int sqrt(1-sin2x)