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Консультация № 176487

04.02.2010, 15:01

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0 5 1

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Обсуждение

Неизвестный

05.02.2010, 16:04

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Я извиняюсь хотел поставить оценку 5 а по ошибке поставил 3

давно

Гордиенко Андрей Владимирович

Мастер-Эксперт
17387
18353

05.02.2010, 18:05

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Верещака Андрей Павлович:
Не смертельно, конечно, но обидно...

Об авторе:
Facta loquuntur.

давно

Гордиенко Андрей Владимирович

Мастер-Эксперт
17387
18353

05.02.2010, 20:20

общий

это ответ

Здравствуйте, Верещака Андрей Павлович.

1. 4 + 2x – x² = -(x² – 2x – 4) = -(x – 1 + √5)(x – 1 – √5),
x – 1 + √5 = t², dx = 2tdt, x – 1 – √5 = t² – 2√5,
∫dx/√(4 + 2x – x²) = -∫dx/√(( x – 1 + √5)( x – 1 – √5)) = -2∫tdt/√(t²(t² – 2√5)) = -2∫dt/√(t² – 2√5) =
= -2ln |t + √(t² – 2√5)| + C = -2ln |√(x – 1 + √5) + √(x – 1 – √5)| + C.

2. x = t², dx = 2tdt, √x = t,
∫(3√x + 1)dx/(√x + 3) = 2∫t(3t + 1)dt/(t + 3) = 2∫(3t² + t)dt/(t + 3),
(3t² + t)/(t + 3) = 3t – 8 + 24/(t + 3),
2∫(3t² + t)dt/(t + 3) = 6∫tdt – 16∫dt + 48∫dt/(t + 3) = 3t² – 16t + 48ln |t + 3| + C =
= 3x – 16√x + 48ln |√x + 3| + C.

3. u = x, du = dx, e^x/2dx = dv, v = ∫e^x/2dx = 2e^x/2,
∫xe^x/2dx = 2xe^x/2 – 2∫e^x/2dx + C = 2xe^x/2 – 2e^x/2 + C = 2e^x/2(x – 1) + C.

С уважением.

5

Спасибо огромное, очень подробный и понятный ответ

Об авторе:
Facta loquuntur.

давно

Гордиенко Андрей Владимирович

Мастер-Эксперт
17387
18353

05.02.2010, 20:25

общий

Верещака Андрей Павлович:
Постарайтесь не ошибиться, если будете оценивать ответ повторно.

Об авторе:
Facta loquuntur.

Неизвестный

06.02.2010, 03:55

общий

Теперь оценил по достоинству

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