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Консультация № 140891
28.07.2008, 15:27
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Здравствуйте!
Помогите взять интегральчик: (корень_второй_степени(x)/(корень_третьей_степени(x)+1))dx
Довел его до состояния 6*интеграл(t^8/(t^2+1))dt, что далее смог привести к -6*интеграл(Sin^9(u)/Cos(u))du, а дальше не могу:)
Помогите взять интегральчик: (корень_второй_степени(x)/(корень_третьей_степени(x)+1))dx
Довел его до состояния 6*интеграл(t^8/(t^2+1))dt, что далее смог привести к -6*интеграл(Sin^9(u)/Cos(u))du, а дальше не могу:)
Обсуждение
28.07.2008, 16:09
общий
это ответ
Здравствуйте, Troyan!
Замена x= t^6 - это хорошо, а тригонометрия, пожалуй, ни к чему.
Дальше можно так:
int(t^8/(t^2+1))dt = int ((t^8-1+1)/(t^2+1))dt = int(1/(t^2+1))dt+
int((t^2-1)*(t^2+1)*(t^4+1)/(t^2+1))dt = arctg(t)+int((t^2-1)*(t^4+1))dt=
arctg(t)+int(t^6-t^4+t^2-1)=arctg(t) + t^7/7- t^5/5+ t^3/3-t.
Замена x= t^6 - это хорошо, а тригонометрия, пожалуй, ни к чему.
Дальше можно так:
int(t^8/(t^2+1))dt = int ((t^8-1+1)/(t^2+1))dt = int(1/(t^2+1))dt+
int((t^2-1)*(t^2+1)*(t^4+1)/(t^2+1))dt = arctg(t)+int((t^2-1)*(t^4+1))dt=
arctg(t)+int(t^6-t^4+t^2-1)=arctg(t) + t^7/7- t^5/5+ t^3/3-t.
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