int_(0)^(1)(1)/(2x-3)dx

int_(0)^(1)(dx)/((2x-3))

Show :(2)/(ln3)

int_(0)^(1)(1+2x)dx

int_(0)^(1) (1)/(x^(2) +2x+3)dx

int_(0)^(1) (1)/(x^(2) +2x+3)dx

Evaluate :int_(0)^(1)(1)/(sqrt(2x+3))dx

Evaluate : (i) int_(0)^(1)x(1-x)^(n)dx (ii) int_(0)^(1)x(1-x)^(3//2)dx

int_(0)^(3)(1)/(x^(2)-3x+2)dx

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 .