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Консультация № 187443
06.06.2013, 12:02
84.74 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас помочь в решении задачи:
Найти неопределенные интегралы:
Найти неопределенные интегралы:
Обсуждение
06.06.2013, 12:12
общий
это ответ
Здравствуйте, Посетитель - 369100!
∫2x(x^2+1)^5 dx=[(u=x^2+1; du=2xdx)]=∫u^5 du=u^6/6+C=(x^2+1)^6/6+C
∫x^2 cos(x/2)dx=uv-∫vdu=[(u=x^2; du=2xdx; dv=cos(x/2)dx; v=2 sin(x/2) )]=2x^2 sin(x/2)-4∫x sin(x/2)dx=uv-∫vdu=[(u=x; du=dx; dv=sin(x/2)dx; v=-2 cos(x/2) )]=2x^2 sin(x/2)+8x cos(x/2)-8∫cos(x/2)dx=2x^2 sin(x/2)+8x cos(x/2)-16 sin(x/2)+C
∫2x(x^2+1)^5 dx=[(u=x^2+1; du=2xdx)]=∫u^5 du=u^6/6+C=(x^2+1)^6/6+C
∫x^2 cos(x/2)dx=uv-∫vdu=[(u=x^2; du=2xdx; dv=cos(x/2)dx; v=2 sin(x/2) )]=2x^2 sin(x/2)-4∫x sin(x/2)dx=uv-∫vdu=[(u=x; du=dx; dv=sin(x/2)dx; v=-2 cos(x/2) )]=2x^2 sin(x/2)+8x cos(x/2)-8∫cos(x/2)dx=2x^2 sin(x/2)+8x cos(x/2)-16 sin(x/2)+C
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