int(dx)/(root(3)(x^(5/2)(x+1)^(7/2)))

If I=int(dx)/(root(3)(x^((5)/(2))(1+x)^((7)/(2))))=kf(x)+c , where c is the integration constant and f(1)=(1)/(2^((1)/(6))) , then the value of f(2) is

int(dx)/(root(3)((x-1)^(4)*(x+1)^(2)))

int(1)/(root(3)(x^(2)))dx

"int(x-1)/(root(3)(x^(2)))dx

int(1)/(root(3)(x^2))dx

int(dx)/((x^((5)/(2))(x+1)^((7)/(2)))^((1)/(3)))

int root(3)(x^(2))dx

int((sqrt(x)+root(3)(x^(2)))^(2))/x dx=

int((sqrt(x)+root(3)(x^(2)))^(2))/x dx=

int x^(2)root(5)(x^(3)+2)dx