Помогите с интегралом, пожалуйста
int (ln 3^(1/2) ln 24^(1/2)) (1 + e^(2x))^(1/2) dx

int (ln 3^(1/2) ln 24^(1/2)) (1 + e^(2x))^(1/2) dx =
= | t = (1 + e^(2x))^(1/2); 1 + e^(2x) = t^2; e^(2x) = t^2 - 1; 2x = ln (t^2 - 1);
x = 1/2 * ln (t^2 - 1); dx = 1/2 * 1/(t^2 - 1) * 2t dt = t/(t^2 - 1) dt | =
= int (2 5) t * t/(t^2 - 1) dt = int (2 5) t^2/(t^2 - 1) dt =
= int (2 5) (t^2 - 1 + 1)/(t^2 - 1) dt =
= int (2 5) dt + int (2 5) dt/(t^2 - 1) = (t)_{2}^{5} + int (2 5) dt/((t - 1) * (t + 1)) =
= 5 - 2 + 1/2 * int (2 5) 2 dt/((t - 1) * (t + 1)) =
= 3 + 1/2 * int (2 5) ((t + 1) - (t - 1))/((t - 1) * (t + 1)) dt =
= 3 + 1/2 * int (2 5) dt/(t - 1) - 1/2 * int (2 5) dt/(t + 1) =
= 3 + 1/2 * (ln |t - 1|)_{2}^{5} - 1/2 * (ln |t + 1|)_{2}^{5} =
= 3 + 1/2 * ln 4 - 1/2 * ln 1 - 1/2 * ln 6 + 1/2 * ln 3 = 3 + 1/2 * ln 2.

Всё...разобрался. Спасибо большое (IMG:style_emoticons/default/smile.gif)