Number of integral values of k so that `int_(1)^(k)(1+(3x-2)/(2sqrt(x)))dx<4sqrt(k)`

The number of integral values of k for which the equation sin^(-1)x+tan^(-1)x=2k+1 has a solution is

The value of the integral int_(-1)^(1)log(x+sqrt(x^(2)+1))dx is

The value of the integral int_(0)^(a) (1)/(x+sqrt(a^(2)-x^(2)))dx , is

The number of integral values of K' the inequality |(x^2+kx+1)/(x^2+x+1)|<3 is satisfied for all real values of x is....

The value of integral int_(0)^(1)sqrt((1-x)/(1+x)) dx is

The number of integral values of k for which the equation sin ^−1 x+tan −1 x=2k+1 has a solutions is:

The value of the integral I=int_(1)^(oo) (x^(2)-2)/(x^(3)sqrt(x^(2)-1))dx , is

The value of the integral int_(-1)^(1) (x-[2x]) dx,is

The value of int_(-1)^(1) {sqrt(1+x+x^(2))-sqrt(1-x+x^(2))}dx , is

The value of the integral int_(0)^(1) (1)/((1+x^(2))^(3//2))dx is