angela
Сообщение
#8000 27.11.2007, 20:29
Помогите, пожалуйста, найти интеграл
int ln (2 * x + 3) dx
Dimka
Сообщение
#8002 27.11.2007, 21:00
int ln (2 * x + 3) dx = x * ln (2 * x + 3) - int x d(ln (2 * x + 3)) =
= x * ln (2 * x + 3) - int x * (ln (2 * x + 3))' dx =
= x * ln (2 * x + 3) - int x * 1/(2 * x + 3) * (2 * x + 3)' dx =
= x * ln (2 * x + 3) - int x * 1/(2 * x + 3) * 2 dx =
= x * ln (2 * x + 3) - int 2 * x/(2 * x + 3) dx =
= x * ln (2 * x + 3) - int x/(x + 3/2) dx =
= x * ln (2 * x + 3) - int (x + 3/2 - 3/2)/(x + 3/2) dx =
= x * ln (2 * x + 3) - int dx + 3/2 * int dx/(x + 3/2) =
= x * ln (2 * x + 3) - x + 3/2 * ln |x + 3/2| + C