osipvs
Сообщение
#2800 4.5.2007, 14:21
помогите пожалуйста, что-то совсем запутался
int (1/3 1/2) x dx/(x - 1)^3
Lion
Сообщение
#2801 4.5.2007, 14:52
int (1/3 1/2) x dx/(x - 1)^3 = int (1/3 1/2) x d(-1/2 * 1/(x - 1)^2) =
= -1/2 * int (1/3 1/2) x d(1/(x - 1)^2) =
= -1/2 * (x * 1/(x - 1)^2)_{1/3}^{1/2} + 1/2 * int (1/3 1/2) 1/(x - 1)^2 dx =
= -1/2 * (1/2 * 1/(1/2 - 1)^2 - 1/3 * 1/(1/3 - 1)^2) - 1/2 * (1/(x - 1))_{1/3}^{1/2} =
= -1/2 * (1/2 * 4 - 1/3 * 9/4) - 1/2 * (1/(1/2 - 1) - 1/(1/3 - 1)) =
= -1/2 * (2 - 3/4) - 1/2 * (-2 + 3/2) = -1/2 * 5/4 - 1/2 * (-1/2) = -5/8 + 1/4 = -3/8.