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Консультация № 137981
27.05.2008, 09:12
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Уважаемые эксперты! Помогите, пожалуйста, решить задачу по высшей математике...
Задача:
Вычислить неопределенный интеграл.
∫xdx/5x^2+1
Добавляйте коментарии к вычеслениям...
Заранее спасибо...
Задача:
Вычислить неопределенный интеграл.
∫xdx/5x^2+1
Добавляйте коментарии к вычеслениям...
Заранее спасибо...
Обсуждение
Неизвестный
27.05.2008, 11:57
общий
это ответ
Здравствуйте, Уманский Денис!
Внесем до множим наш интеграл на 10 и разделим на 10
0.01 * ∫(10*x)dx/(5x^2+1) (внесем 10*x под знак интеграла 10*x *dx=(5*x^2) если продифференцировать то получиться опять 10*x, так же d(5x^2)=d(5x^2+1), тоже если продифференцировать, то получиться одно и тоже)
И тогда:
∫xdx/5x^2+1=
=0.01 * ∫(10*x)dx/(5x^2+1)
=0.01∫d(5x^2 +1)/(5x^2+1) = 0.01 ln (5x^2+1) + C
Приложение:
Можно также вместо константу написать в виде 0.01* lnC и сложить ее с логарифмом, тогда будет 0.01 *ln(5x^2 +1) 0.01 lnC= 0.01 ln[C *(5x^2+1)]
Внесем до множим наш интеграл на 10 и разделим на 10
0.01 * ∫(10*x)dx/(5x^2+1) (внесем 10*x под знак интеграла 10*x *dx=(5*x^2) если продифференцировать то получиться опять 10*x, так же d(5x^2)=d(5x^2+1), тоже если продифференцировать, то получиться одно и тоже)
И тогда:
∫xdx/5x^2+1=
=0.01 * ∫(10*x)dx/(5x^2+1)
=0.01∫d(5x^2 +1)/(5x^2+1) = 0.01 ln (5x^2+1) + C
Приложение:
Можно также вместо константу написать в виде 0.01* lnC и сложить ее с логарифмом, тогда будет 0.01 *ln(5x^2 +1) 0.01 lnC= 0.01 ln[C *(5x^2+1)]
Форма ответа
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