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Консультация № 109251
13.11.2007, 17:38
0.00 руб.
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Интеграл:
6: S x^2*dx/x^2+3x+3
Приложение:
S - условное обозначение интеграла.
6: S x^2*dx/x^2+3x+3
Приложение:
S - условное обозначение интеграла.
Обсуждение
Неизвестный
13.11.2007, 22:04
общий
это ответ
Здравствуйте, Packbar!
∫x²dx/(x²+3x+3) =
∫[(x²+3x+3)-3/2*(2x+3)+3/2]dx/(x²+3x+3) =
∫dx – 3/2∫(2x+3)dx/(x²+3x+3) + 3/2∫dx/(x²+3x+3) =
x – 3/2∫d(x²+3x+3)/(x²+3x+3) + 3/2∫dx/((x+3/2)²+(√3/2)²) =
x – 3/2*ln|x²+3x+3| + 3/2 * 2/√3*arctg((x+3/2)/(√3/2)) + C =
x – 3/2*ln|x²+3x+3| + √3*arctg((2x+3)/√3) + C.
∫x²dx/(x²+3x+3) =
∫[(x²+3x+3)-3/2*(2x+3)+3/2]dx/(x²+3x+3) =
∫dx – 3/2∫(2x+3)dx/(x²+3x+3) + 3/2∫dx/(x²+3x+3) =
x – 3/2∫d(x²+3x+3)/(x²+3x+3) + 3/2∫dx/((x+3/2)²+(√3/2)²) =
x – 3/2*ln|x²+3x+3| + 3/2 * 2/√3*arctg((x+3/2)/(√3/2)) + C =
x – 3/2*ln|x²+3x+3| + √3*arctg((2x+3)/√3) + C.
Форма ответа
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