Помогите, пожалуйста, вычислить интеграл
int (2^(1/2) +00) dx/(x * (x^2 - 1)^(1/2))

int (2^(1/2) +00) dx/(x * (x^2 - 1)^(1/2)) =
= | (x^2 - 1)^(1/2) = t, x^2 = t^2 + 1, x = (t^2 + 1)^(1/2),
dx = 1/2 * (t^2 + 1)^(-1/2) * (t^2 + 1)' dt = t/(t^2 + 1)^(1/2) dt | =
= int (1 +00) 1/((t^2 + 1)^(1/2) * t) * t/(t^2 + 1)^(1/2) dt =
= int (1 +00) t/((t^2 + 1) * t) dt = int (1 +00) dt/(1 + t^2) =
= lim (a->+00) int (1 a) dt/(1 + t^2) = lim (a->+00) (arctg t)_{1}^{a} =
= lim (a->+00) (arctg a - arctg 1) = lim (a->+00) arctg a - arctg 1 =
= pi/2 - pi/4 = pi/4.

Спасибо огромное))))