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Консультация № 137142
16.05.2008, 21:31
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Уважаемые эксперты! Помогите, пожалуйста решить неопределенный интеграл dx/5+3x.
Спасибо.
Спасибо.
Обсуждение
Неизвестный
17.05.2008, 13:47
общий
это ответ
Здравствуйте, Dasha Kotova!
инт(dx/(5+3x))=1/3*(инт(d(5+3x)/(5+3x)))=1/3*ln|5+3x|+C
Т.е., вносим под знак дифференциала недостающую функцию - в данном случае это (5+3x), за интеграл придется вынести 1/3, т.к. d(5+3x)=3 - значение же выражения должно остаться неизменным. В результате преобразований получаем интеграл от табличной функции dx/x=ln|x|+C. В вашем случае за х принято (5+3x)
инт(dx/(5+3x))=1/3*(инт(d(5+3x)/(5+3x)))=1/3*ln|5+3x|+C
Т.е., вносим под знак дифференциала недостающую функцию - в данном случае это (5+3x), за интеграл придется вынести 1/3, т.к. d(5+3x)=3 - значение же выражения должно остаться неизменным. В результате преобразований получаем интеграл от табличной функции dx/x=ln|x|+C. В вашем случае за х принято (5+3x)
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