(1)/(9)x^(2)-2x-9

For x in(0,1) arrange f_(1)(x) = (1)/(9-x^(2)), f_(2)(x) = (1)/(9-2x^(2)) and f_(3)(x) = (1)/(9-x^(2)-x^(3)) in ascending order and hence prove that 1/6 ln2 lt int_(0)^(1)(1)/(9-x^(2)-x^(3)) dx lt (1)/(6sqrt(2)) ln 5 .

For x in(0,1) arrange f_(1)(x) = (1)/(9-x^(2)), f_(2)(x) = (1)/(9-2x^(2)) and f_(3)(x) = (1)/(9-x^(2)-x^(3)) in ascending order and hence prove that 1/6 ln2 lt int_(0)^(1)(1)/(9-x^(2)-x^(3)) dx lt (1)/(6sqrt(2)) ln 5 .

Q.If x be real,then find the range of the following rational expressions (i) (x^(2)+x+1)/(x^(2)+1) (i) y=(x^(2)-2x+9)/(x^(2)-2x-9)

Solve equation : 9(x^(2)+(1)/(x^(2)))-9(x+(1)/(x))-52=0

(1) / (3) x ^ (2) -2x-9

9*int(x+1)/(x^(2)+2x+1)dx

9. int(x+1)/(x^(2)+2x+2)dx

(x)/(x^(2)-5x+9)<=1

int (1)/((x^(2)+9)sqrt(x^(2)-9))dx=