" 8."sin^(-1)(x sqrt(x)),0<=x<=1

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

If y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))) and 0

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))

Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x))/2}=pi/2-(sin^(-1)x)/2,""0 < x < 1

Differentiate sin^(-1){(sqrt(1+x)+sqrt(1-x))/2},\ \ 0

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

Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x))/(2)}=(pi)/(4)+(sin^(-1)x)/(2),0

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