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Консультация № 137978
27.05.2008, 09:09
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Уважаемые эксперты! Помогите, пожалуйста, решить задачу по высшей математике...
Задача:
Вычислить неопределенный интеграл.
∫dx/(2+x)^3
Добавляйте коментарии к вычеслениям...
Заранее спасибо...
Задача:
Вычислить неопределенный интеграл.
∫dx/(2+x)^3
Добавляйте коментарии к вычеслениям...
Заранее спасибо...
Обсуждение
Неизвестный
27.05.2008, 12:08
общий
это ответ
Здравствуйте, Уманский Денис!
Можно написать что dx=d(x+2) как я делал в предыдущих ответах, а можно заменить 2+x на t:
t=2+x
dt=dx
то есть получается d(x+2)=dx, то есть можно делать замены переменных, а можно вносить что-либо под знак дифференциала, смысл ход решения почти одниковы
∫dx/(2+x)^3 = ∫dt/(t)^3=∫dt *t^-3 = -2*t^-2 +C= -2/t^2 +C = -2/(x+2) +С
Можно написать что dx=d(x+2) как я делал в предыдущих ответах, а можно заменить 2+x на t:
t=2+x
dt=dx
то есть получается d(x+2)=dx, то есть можно делать замены переменных, а можно вносить что-либо под знак дифференциала, смысл ход решения почти одниковы
∫dx/(2+x)^3 = ∫dt/(t)^3=∫dt *t^-3 = -2*t^-2 +C= -2/t^2 +C = -2/(x+2) +С
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