If `(3 sqrt3 + 5)^(2n +1) = x ` and f = x - [x] where [x] is integral part of x, find the value of xf.

If x = 2 - sqrt 3 , find the value of (x-1/x)^3

If x=1-sqrt(2) , find the value of (x-1/x)^3

If x=1-sqrt(2), find the value of (x-1/x)^3

Let f(n) = [1/2 + n/100] where [x] denote the integral part of x. Then the value of sum_(n=1)^100 f(n) is

Let f(x) = x-[x] , for every real number x, where [x] is integral part of x. Then int_(-1) ^1 f(x) dx is

If x = sqrt(3)- sqrt(2) find the value of x+(1)/(x)

If x-1/x=3+2sqrt(2) , find the value of x^3-1/(x^3)

If x-1/x=3+2sqrt(2) , find the value of x^3-\ 1/(x^3)

If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f (x))/(sqrt2-f (x))|+C where f (x) = sin x + cos x find the value of (12A+9sqrt2V)-3.

If the integral I=inte^(x^(2))x^(3)dx=e^(x^(2))f(x)+c , where c is the constant of integration and f(1)=0 , then the value of f(2) is equal to