find the value of `sqrt(xsqrt(xsqrt(x.......)))`

Evaluate : (a) sqrt(xsqrt(xsqrt(x.....oo))) (b) sqrt(6+ sqrt(6 + sqrt(6 + ......oo))) (c) sqrt(a^(3)root(3)(b sqrt(a^(3) root(3)(b.......oo))))

int(dx)/(sqrt(x)+xsqrt(x))

The value of sin^(-1)[xsqrt(1-x)+sqrt(x)sqrt(1-x^2)] is equal to

The value of sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)] is equal to

Evaluate: int1/xsqrt((1-sqrt(x))/(1+sqrt(x))dx)

The value of int_(1)^(4)(dx)/(xsqrt(x)) is-

If xsqrt2=1+sqrt-1, "find the value of " x^(6)+x^(4)+x^(2)+2.

int (dx)/(xsqrt(1+x^(3)))

or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect to tan^(-1) ((2xsqrt(1-x^2))/(1-2x^2)) at x=0.

Solve: x^(x.sqrt(x))=(xsqrt(x))^(x)