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Консультация № 109253
13.11.2007, 17:42
0.00 руб.
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1
1
Решить интеграл:
8: S xarcctg*dx
Приложение:
S - условное обозначение интеграла.
8: S xarcctg*dx
Приложение:
S - условное обозначение интеграла.
Обсуждение
Неизвестный
13.11.2007, 18:02
общий
это ответ
Здравствуйте, Packbar!
S xarcctg*dx=|интегрирование по частям|=|u=arcctgx,du=-dx/(1+x^2),dv=xdx,v=x^2/2|=
=arcctgx*(x^2/2)+1/2*S x^2/(1+x^2)*dx=arcctgx*(x^2/2)+1/2*S (x^2+1-1)/(1+x^2)*dx=
=arcctgx*(x^2/2)+1/2*S (1-1/(1+x^2))*dx=arcctgx*(x^2/2)+1/2x-1/2arctgx+C
S xarcctg*dx=|интегрирование по частям|=|u=arcctgx,du=-dx/(1+x^2),dv=xdx,v=x^2/2|=
=arcctgx*(x^2/2)+1/2*S x^2/(1+x^2)*dx=arcctgx*(x^2/2)+1/2*S (x^2+1-1)/(1+x^2)*dx=
=arcctgx*(x^2/2)+1/2*S (1-1/(1+x^2))*dx=arcctgx*(x^2/2)+1/2x-1/2arctgx+C
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