int (x^2 - a^2)^(1/2)/x dx =
= | t = (x^2 - a^2)^(1/2), dt = 1/2 * (x^2 - a^2)^(-1/2) * 2 * x dx =>
=> dx = (x^2 - a^2)^(1/2)/x dt = t/x dt, t^2 = x^2 - a^2 | =
= int t/x * t/x dt = int t^2/x^2 dt = int t^2/(t^2 + a^2) dt =
= int (t^2 + a^2 - a^2)/(t^2 + a^2) dt =
= int dt - a^2 * int dt/(t^2 + a^2) = t - a^2 * 1/a * arctg (t/a) + C =
= | t = (x^2 - a^2)^(1/2) | =
= (x^2 - a^2)^(1/2) - a * arctg ((x^2 - a^2)^(1/2)/a) + C