Prove that `pi/6leint_0^1dx/sqrt(4-x^2-x^3)lepi/(4sqrt(2))`

Prove that pi/6

Prove that pi/6 lt int_0^1(dx) (sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

int_0^2sqrt(6x+4)dx

Prove that : int_(0)^(a) (dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)

Prove that tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))]=pi/4+1/2cos^(-1)x^2

Prove that : int_(0)^(1) (log x)/(sqrt(1-x^(2)))dx=-(pi)/(2)log 2

Prove that 4le int_(1)^(3) sqrt(3+x^(3)) dx le 2sqrt30 .

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

Prove that ln 2 lt int_(0)^(1)(dx)/(sqrt(1+x^(4))) lt (pi)/2)

Prove that 4 lt= int_1^3 sqrt(3+x^2) dx lt= 4sqrt(3)