The value of the integral `int_alpha^beta 1/(sqrt((x-alpha)(beta-x)))dx`

The value of the integral int_(alpha)^(beta) sqrt((x-alpha)(beta-x))dx , is

int(dx)/(sqrt((x-alpha)(beta-x)))

int _(alpha)^(beta) sqrt((x-alpha)/(beta -x)) dx is equal to

int(dx)/((x-alpha)sqrt((x-alpha)(x-beta)))

int(dx)/((x-beta)sqrt((x-alpha)(beta-x))) is

If alpha and beta are solutions of the equation 4log_(3)^(2)x-4log_(3)x^(2)+1=0 then the value of |(sqrt(alpha beta)+1)/(sqrt(alpha beta)-1)| is

int(dx)/(sin(x-alpha)sin(x-beta))

If the value of the integral int_0^5 (x + [x])/(e^(x - [x])) dx = alphae^(-1) + beta ,where alpha, beta in R, 5alpha + 6beta = 0, and [x] denotes the greatest integer less than or equal to x, then the value of (alpha + beta )^2 is equal to :

Evaluate: int(1)/((x-alpha)(beta-x))dx,(beta>alpha)