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Задать вопрос экспертам

Консультация № 109172

13.11.2007, 08:55

0.00 руб.

0 2 2

Образование

Прива эксперты!
Помогите с интегралами:
1: S a^x(3+(a^-x/x^5))*dx
2: S 7dx/(sqrt^3(3-2x))
3: S 2cosx*dx/7-3sinx
4: S e^-x^2*xdx
5: S (sqrt4-3lnx)*dx/x
6: S x^2*dx/x^2+3x+3
7: S (7x-15/x^3-2x^2+5x)*dx
8: S xarcctg*dx
9: S sin^2*x*dx
10: S dx/x^2*(sqrt 1+x^2)

Приложение:
S - условное обозначение интеграла. Во всех примерах где написано sqrt - это корень; во 2 примере корень находится в 3 степени; в 4 примере "e" в степени -x в квадрате

Обсуждение

Неизвестный

13.11.2007, 09:53

общий

это ответ

Здравствуйте, Packbar!
9: S sin^2*x*dx=S 1/2*(1-cos2x)dx=1/2x-1/2 S cos2x dx=1/2 x-1/2*1/2*sin2x+C=
=x/2- (sin2x)/4+C

P.S. sin^2x=1/2(1-cos2x)

Неизвестный

16.11.2007, 05:23

общий

это ответ

Здравствуйте, Packbar!
5: ∫[√(4-3lnx)/x]dx = (вносим 1/х под знак дифференциала) = ∫√(4-3lnx)d(lnx) = (делаем замену переменных t = lnx) = ∫√(4-3t)dt = (-1/3)∫√(4-3t)d(4-3t) = (-2/9)√(4-3t)³ + C = (-2/9)√(4-3lnx)³ + C

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