int (ln 2 2ln 2) dx/(e^x - 1)
e^x -1 = t
e^x = t + 1
x = ln (t + 1)
dx = dt/(t + 1)
x = 2ln 2 => t=3
x = ln 2 => t=1
Получается int (1 3) dt/((t + 1) * t), а дальше торможу. Помогите, пожалуйста.

int (ln 2 2ln 2) dx/(e^x - 1) = | t = e^x - 1, e^x = t + 1, x = ln (t + 1), dx = dt/(t + 1) | =
= int (1 3) dt/((t + 1) * t) = int (1 3) ((t + 1) - t)/((t + 1) * t) dt =
= int (1 3) dt/t - int (1 3) dt/(t + 1) = (ln |t|)_{1}^{3} - (ln |t + 1|)_{1}^{3} =
= (ln 3 - ln 1) - (ln 4 - ln 2) = ln 3 - ln 4 + ln 2 = ln 3/2.

Спасибо большое.