`sqrt(xsqrt(2^(x) x^2sqrt(3^(x^(3)) x^3sqrt(6^(x^(6)) x^4sqrt(9^(x^(10))))))) =`

sqrt(x sqrt(2^(x)x^(2)sqrt(3^(x^(3))x^(3)sqrt(6^(x^(6))x^(4)sqrt(9^(x^(10)))))))

sqrt(3x^(2))+11x+6sqrt(3)

x^2+3sqrt(3)x+6

y = sqrt(xsqrt(x^(2)sqrt(x^(3)sqrt(x^(4)sqrt(x^(5).....oo))))), then (dy/dx) at x = 2 is equal to

int(x+3sqrt(x^(2))+6sqrt(x))/(x(1+3sqrt(x)))dx

6sqrt(3)x^(2)-47x+5sqrt(3)

Evaluate int ((""^(3)sqrt(x+sqrt(2-x ^(2))))(""^(6)sqrt(1-xsqrt(2-x ^(2))))dx)/(""^(3) sqrt(1-x ^(2))), x in (0,1):

Evaluate int ((""^(3)sqrt(x+sqrt(2-x ^(2))))(""^(6)sqrt(1-xsqrt(2-x ^(2))))dx)/(""^(3) sqrt(1-x ^(2))), x in (0,1):