8_(p)(sin x)^(x)+sin^(-1)sqrt(x)

"Differentiate: "(sin x)^(x)+sin^(-1)sqrt(x)

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

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

If y=sin^(-1)(xsqrt(1-x)+sqrt(x)sqrt(1-x^2)) and (dy)/(dx)=1/(2sqrt(x(1-x)))+p , then p is equal to 0 (b) 1/(sqrt(1-x)) sin^(-1)sqrt(x) (d) 1/(sqrt(1-x^2))

intsqrt(x/(1-x))\ dx is equal to (a) 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

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

If sin^(-1)x+sin^(-1)(1-x)=sin^(-1)sqrt(1-x^(2)), then x is equal to

(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]

Evaluate: int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x))\ dx