Помогите, пожалуйста, найти интеграл
int dx/(x * (x^2 + 1)^(1/2))

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

Спасибо (IMG:style_emoticons/default/smile.gif)