[19.sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))]],[=sin^(-1)x-sin^(-1)sqrt(x)]

(d)/(dx)[sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))] is

sin^(-1)x+sin^(-1)sqrt(1-x^(2))

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

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x

cos^(-1)sqrt(1-x)+sin^(-1)sqrt(1-x)=

sin^(-1)sqrt(x)+cos^(-1)sqrt(1-x)=

sin^(-1)sqrt(x)+cos^(-1)sqrt(1-x)=

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

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

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