If `int_((1)/(3))^(3)(tan^(-1)x)/(x)dx=(pi)/(8)" lnk`, then value of `(k)/(4)` is equal to

If int_(0)^(1)(tan^(-1)x)/(x)dx=k int_(0)^( pi/2)(x)/(sin x)dx then the value of k is

The value of int_(1)^(4) |x-3|dx is equal to

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

If the value of the integral I=int_(0)^(1)(dx)/(x+sqrt(1-x^(2))) is equal to (pi)/(k) , then the value of k is equal to

int_(0)^(pi//4)(tan^(3)x)/((1+cos2x))dx

If int_(0)^(1)(tan^(-1)x)/(x)dx=k int_(0)^( pi/2)(x)/(sin x)dx then k=

int_(pi//6)^(pi//3)(1)/(1+tan x) dx=

If int_((-1)/(sqrt3))^(1//sqrt3)(x^(4))/(1-x^(4))cos^(-1)((2x)/(1+x^(2)))dx=k , then int_(0)^(1//sqrt3)(x^(4))/(1-x^(4))dx the value of k is equal to

int_(0)^((pi)/(3))(tan x)/(sqrt(2k sec x))dx=1-(1)/(sqrt(2)), then value of k is (a) 2 (b) 1 (b) 1 (d) (1)/(4)