Добрый день, помогите, пожалуйста, найти интеграл
int (e^x + 1)^(-1/2) dx.
Заранее спасибо.

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