Грета
Сообщение
#11483 23.2.2008, 18:03
Помогите, пожалуйста, найти интеграл
int x/(x + 4)^(1/2) dx
Ярослав_
Сообщение
#11486 23.2.2008, 18:11
int x/(x + 4)^(1/2) dx = int (x + 4 - 4)/(x + 4)^(1/2) dx =
= int (x + 4)^(1/2) dx - 4 * int dx/(x + 4)^(1/2) =
= int (x + 4)^(1/2) dx - 4 * int (x + 4)^(-1/2) dx =
= 1/(1/2 + 1) * (x + 4)^(1/2 + 1) - 4 * 1/(-1/2 + 1) * (x + 4)^(-1/2 + 1) + C =
= 2/3 * (x + 4)^(3/2) - 8 * (x + 4)^(1/2) + C =
= 2/3 * (x + 4)^(1/2) * (x + 4 - 12) + C = 2/3 * (x - 8) * (x + 4)^(1/2) + C