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Консультация № 67151
15.12.2006, 18:29
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Уважаемые эксперты, пожалуйста, помогите, если вас не затруднит, решить задания!
С помощью соответствующей замены переменной интегрирования (подстановки) найти интегралы:
1. ∫ ^7 √(sin^2 x) cosx dx
2. ∫ x^3 dx / x^8 +16
3. ∫ 2^(x^2+3) x dx
С помощью соответствующей замены переменной интегрирования (подстановки) найти интегралы:
1. ∫ ^7 √(sin^2 x) cosx dx
2. ∫ x^3 dx / x^8 +16
3. ∫ 2^(x^2+3) x dx
Обсуждение
Неизвестный
15.12.2006, 19:16
общий
это ответ
Здравствуйте, XDRIVE!
1. ∫sin^(2/7)x * cosx dx = ∫sin^(2/7)x dsinx = 7/9 sin^(9/7)x + C.
Здесь неявная замена t = sin x.
2. Замена x^4 = t
∫ x^3 dx / (x^8+16) = 1/4 ∫d(x^4) / ((x^4)^2 + 16) = 1/16 arctg (x/4) + C.
3. Заменить x^2 + 3
∫2^(x^2+3)xdx = 1/2 ∫2^(x^2+3)d(x^2+3) = 2^(x^2 + 2) / ln2 + C.
Удачи!
1. ∫sin^(2/7)x * cosx dx = ∫sin^(2/7)x dsinx = 7/9 sin^(9/7)x + C.
Здесь неявная замена t = sin x.
2. Замена x^4 = t
∫ x^3 dx / (x^8+16) = 1/4 ∫d(x^4) / ((x^4)^2 + 16) = 1/16 arctg (x/4) + C.
3. Заменить x^2 + 3
∫2^(x^2+3)xdx = 1/2 ∫2^(x^2+3)d(x^2+3) = 2^(x^2 + 2) / ln2 + C.
Удачи!
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