Malvina
Сообщение
#4315 3.6.2007, 21:27
Не получается решить до конца пример(
int (x + (1 + x)^(1/2))/(1 + x)^(1/3) dx
Владимир
Сообщение
#4318 3.6.2007, 21:44
int (x + (1 + x)^(1/2))/(1 + x)^(1/3) dx =
= int (x + 1 + (1 + x)^(1/2) - 1)/(1 + x)^(1/3) dx =
= int ((1 + x)^(2/3) + (1 + x)^(1/2 - 1/3) - (1 + x)^(-1/3)) dx =
= int ((1 + x)^(2/3) + (1 + x)^(1/6) - (1 + x)^(-1/3)) dx =
= 1/(2/3 + 1) * (1 + x)^(2/3 + 1) + 1/(1/6 + 1) * (1 + x)^(1/6 + 1) -
- 1/(-1/3 + 1) * (1 + x)^(-1/3 + 1) + C =
= 3/5 * (1 + x)^(5/3) + 6/7 * (1 + x)^(7/6) - 3/2 * (1 + x)^(2/3) + C