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Консультация № 182865
16.04.2011, 18:41
44.77 руб.
0
7
2
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
вычислить несобственный интеграл или доказать его расходимость dx/(x*sqrt(ln x))
вычислить несобственный интеграл или доказать его расходимость dx/(x*sqrt(ln x))
Обсуждение
16.04.2011, 20:12
общий
Адресаты:
Уважаемый Роман, Вы дали неверный ответ. Если Вы выберете x1=1 и x2=e, то получите сходящийся интеграл.
17.04.2011, 14:26
общий
Адресаты:
Дмитрий Германович, ответ дадите? 
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
18.04.2011, 00:36
общий
это ответ
Здравствуйте, Марина!
После замены u=ln x получаем интеграл
[$8747$]1[$8734$]du/[$8730$]u
Это табличный степеной интеграл
[$8747$]1[$8734$]du/u[$945$]
который сходится при [$945$]>1 расходится в противоположном случае. У нас [$945$]=1/2<1. Следовательно, интеграл расходится.
После замены u=ln x получаем интеграл
[$8747$]1[$8734$]du/[$8730$]u
Это табличный степеной интеграл
[$8747$]1[$8734$]du/u[$945$]
который сходится при [$945$]>1 расходится в противоположном случае. У нас [$945$]=1/2<1. Следовательно, интеграл расходится.
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