" 13."y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)]

if y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)] then prove that (1)/(2sqrt(x)sqrt(1-x))

[" 0.",int sin^(-1)sqrt((x)/(a+x))dx" is equal to "],[," 1) "(x+a)tan^(-1)sqrt((x)/(a))-sqrt(ax)+C],[" 3) "(x+a)cot^(-1)sqrt((x)/(a))-sqrt(ax)+C," 2) "(x+a)tan^(-1)sqrt((x)/(a))+sqrt(ax)+C]

Differentiate tan^(-1)[(sqrt(x)+sqrt(a))/(1-sqrt(ax))] w.r.t. x.

y = tan^(-1)((sqrt(x)+sqrt(a))/(1-sqrt(ax))), find dy/dx.

If y =tan ^(-1) ((sqrt( a) -sqrt(x)) /( 1+sqrt( ax)) ) ,then (dy)/(dx)=

If y =tan ^(-1) ((sqrt( a) -sqrt(x)) /( 1+sqrt( ax)) ) ,then (dy)/(dx)=

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

int(sqrt(a)-sqrt(x))/(1-sqrt(ax))dx

If x=(sqrt(2a+1)+sqrt(2a-1))/(sqrt(2a+1)-sqrt(2a-1)) , prove that x^(2)-4ax+1=0