Flower11
Сообщение
#2338 21.4.2007, 7:37
Помогите, пожалуйста, решить
int (x^3 + 1)/(x^2 + 2) dx
venja
Сообщение
#2339 21.4.2007, 8:00
int (x^3 + 1)/(x^2 + 2) dx = int (x^3 + 2x - 2x + 1)/(x^2 + 2) dx =
= int (x * (x^2 + 2) - (2x - 1))/(x^2 + 2) dx = int x dx - int (2x - 1)/(x^2 + 2) dx =
= 1/2 * x^2 - int 2x dx/(x^2 + 2) + int dx/(x^2 + 2) =
= 1/2 * x^2 - int d(x^2)/(x^2 + 2) + 1/2^(1/2) * arctg x/2^(1/2) =
= 1/2 * x^2 - int d(x^2 + 2)/(x^2 + 2) + 1/2^(1/2) * arctg x/2^(1/2) =
= 1/2 * x^2 - ln (x^2 + 2) + 1/2^(1/2) * arctg x/2^(1/2) + C