Помогите, пожалуйста, найти интеграл
int dx/(e^x + 1)
int dx/(e^x + 1) = | t = e^x + 1, e^x = t - 1, x = ln (t - 1), dx = dt/(t - 1) | =
= int 1/t * 1/(t - 1) dt = int 1/(t * (t - 1)) dt = int (t - (t - 1))/(t * (t - 1)) dt =
= int 1/(t - 1) dt - int 1/t dt = ln |t - 1| - ln |t| + C = | t = e^x + 1 | =
= ln |e^x| - ln |e^x + 1| + C = x - ln (e^x + 1) + C
Спасибо.
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