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Консультация № 137985
27.05.2008, 09:14
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Уважаемые эксперты! Помогите, пожалуйста, решить задачу по высшей математике...
Задача:
Вычислить неопределенный интеграл.
∫(x+6)cos4xdx
Добавляйте коментарии к вычеслениям...
Заранее спасибо...
Задача:
Вычислить неопределенный интеграл.
∫(x+6)cos4xdx
Добавляйте коментарии к вычеслениям...
Заранее спасибо...
Обсуждение
Неизвестный
27.05.2008, 12:45
общий
это ответ
Здравствуйте, Уманский Денис!
Здесь надо интегрировать по частям:
∫vdu=v*u-∫udv
у нас
v=x+6
dv=dx
du=cos(4x)*dx
u=1/4 *sin(4x)
тогда:
∫(x+6)cos4xdx = 1/4 *sin(4x) *(x+6) - 1/4 ∫sin(4x)dx=
=1/4 *sin(4x) *(x+6) -1/4 ( 1/4 cos(4x)) +C=1/4 *sin(4x)+(x+6) -1/16 *cos(4x) +C
Здесь надо интегрировать по частям:
∫vdu=v*u-∫udv
у нас
v=x+6
dv=dx
du=cos(4x)*dx
u=1/4 *sin(4x)
тогда:
∫(x+6)cos4xdx = 1/4 *sin(4x) *(x+6) - 1/4 ∫sin(4x)dx=
=1/4 *sin(4x) *(x+6) -1/4 ( 1/4 cos(4x)) +C=1/4 *sin(4x)+(x+6) -1/16 *cos(4x) +C
Форма ответа
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