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Консультация № 162518
16.03.2009, 18:57
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Помогите пожалуйста
найти неопределенный интеграл. Проверить результаты дифференцированием.
интеграл(е^(sin^(2)x)*sin2xdx
интеграл arctgx^(1/2)dx
найти неопределенный интеграл. Проверить результаты дифференцированием.
интеграл(е^(sin^(2)x)*sin2xdx
интеграл arctgx^(1/2)dx
Обсуждение
Неизвестный
16.03.2009, 19:51
общий
это ответ
Здравствуйте, Termit11!
Если sin^(2)x означает sin(x) в квадрате, то первый интеграл берется с помощью замены переменной t = sin(x).
exp(sin^(2)x)*sin2xdx = 2*exp(t^2)*sin(x)*cos(x)dx = 2*exp(t^2)*tdt. Если теперь сделать замену u = t^2 то под интегралом получим
exp(u)du. И интеграл равен
exp(u) = exp(t^2) = exp(sin^(2)x)
Если sin^(2)x означает sin(x) в квадрате, то первый интеграл берется с помощью замены переменной t = sin(x).
exp(sin^(2)x)*sin2xdx = 2*exp(t^2)*sin(x)*cos(x)dx = 2*exp(t^2)*tdt. Если теперь сделать замену u = t^2 то под интегралом получим
exp(u)du. И интеграл равен
exp(u) = exp(t^2) = exp(sin^(2)x)
Форма ответа
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