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Консультация № 136542
Обсуждение
15.05.2008, 01:05
общий
это ответ
Здравствуйте, Snapi!
Если я Вас правильно понял, то требуется найти интеграл от выражения u/(1+u) по du. Имеем: u/(1+u)=1-1/(1+u), и Интеграл (udu/(1+u)) = Интеграл (1-1/(1+u))du=Интеграл du - Интеграл (du/(1+u))=u + Интеграл (d(1+u)/(1+u))=u+ln|1+u|+C.
Ответ: u+ln|1+u|+C.
С уважением.
Если я Вас правильно понял, то требуется найти интеграл от выражения u/(1+u) по du. Имеем: u/(1+u)=1-1/(1+u), и Интеграл (udu/(1+u)) = Интеграл (1-1/(1+u))du=Интеграл du - Интеграл (du/(1+u))=u + Интеграл (d(1+u)/(1+u))=u+ln|1+u|+C.
Ответ: u+ln|1+u|+C.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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