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Консультация № 177197
12.03.2010, 04:02
42.70 руб.
0
3
2
Здравствуйте! Помогите, пожалуйста, решить интеграл на тему "Интегрирование тригонометрических функций":
[$8747$]dx/(2sinx - cosx +5)
Спасибо!
Приложение:
[$8747$]dx/(2sinx - cosx +5)
Спасибо!
Приложение:
Обсуждение
12.03.2010, 10:24
общий
это ответ
Здравствуйте, MrSpencer.
В интеграле делаем замену (универсальная подстановка):
tg(x/2)=t ---> dx=2dt/(1+t2), sin x=2t/(1+t2), cos x=(1-t2)/(1+t2)
Получаем
[$8747$]dx/(2sinx - cosx +5)=[$8747$]dt/(3t2+2t+2)=(1/3)[$8747$]d(t+1/3)/[(t+1/3)2+5/9]=
=(1/[$8730$]5)arctg((3t+1)/[$8730$]5)+C=(1/[$8730$]5)arctg((3tx(x/2)+1)/[$8730$]5)+C
В интеграле делаем замену (универсальная подстановка):
tg(x/2)=t ---> dx=2dt/(1+t2), sin x=2t/(1+t2), cos x=(1-t2)/(1+t2)
Получаем
[$8747$]dx/(2sinx - cosx +5)=[$8747$]dt/(3t2+2t+2)=(1/3)[$8747$]d(t+1/3)/[(t+1/3)2+5/9]=
=(1/[$8730$]5)arctg((3t+1)/[$8730$]5)+C=(1/[$8730$]5)arctg((3tx(x/2)+1)/[$8730$]5)+C
5
Неизвестный
12.03.2010, 22:38
общий
это ответ
Здравствуйте, MrSpencer.
Ответ star9491 - не раскрыт до конца. Более подробное и полное решение Вашего интеграла можете забрать здесь: http://files.mail.ru/ZH3507
Ответ star9491 - не раскрыт до конца. Более подробное и полное решение Вашего интеграла можете забрать здесь: http://files.mail.ru/ZH3507
5
Спасибо большое за подробнейшее объяснение решения!
12.03.2010, 23:08
общий
Комин Александр Геннадьевич:
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Удачи!
На портале создан бесплатный(для всех участников портала, в том числе и посетители) файлообменник "Главная странница"-"Мои файлы"(левая панель). Заливайте файлы на него.
Удачи!
Об авторе:
Мне безразлично, что Вы думаете о обо мне, но я рад за Вас - Вы начали думать.
Мне безразлично, что Вы думаете о обо мне, но я рад за Вас - Вы начали думать.
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