Solve for `x`
`1!+2!+3!+………….+(x-1)!+x!=k^(2)` and `k epsilonI`

For what value of k the HCF of x^(2) + x + (5k -1) and x^(2) - 6x + (3k + 11) "is " (x -2) ?

If x - 1 is a factor of x^(5) - 4x^(3) +2 x^(2) - 3x + k = 0 then k is

if (x^(3)-5)/(x^(2)-3x+2)=x+k+(ax+b)/(x^(2)-3x+2) then: (1) the value of k and (2) the value of (a+b+1)/(k) and (3) the value (b^(2)-1)/(40k)

int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k _(1)) ( sqrt(1-9x ^(2))+ (cos ^(-1) 3x )^(k_(2)))+c, then k _(1) ^(2)+k_(2)^(2)= (where C is an arbitrary constnat. )

int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k _(1)) ( sqrt(1-9x ^(2))+ (cos ^(-1) 3x )^(k_(2)))+c, then k _(1) ^(2)+k_(2)^(2)= (where C is an arbitrary constnat. )

int ((2x^(e)+ 3)dx)/((x^(2) -1)(x^(2) + 4)) = k log ((x+1)/(x-1)) +k (tan^(-) ((x)/(2))) , then k equals :