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Консультация № 185795
09.04.2012, 20:08
87.59 руб.
0
4
4
Здравствуйте! Прошу помощи в следующем вопросе:1) [formula] int sin^2*4xdx =;
2) [formula] int sin 7*xdx =;
3) [formula] int tg^7xdx =;
4) [formula] int {-1}{-2/3}{dx/(3x+1)^5} =;
5) [formula] int (x + 1)In2xdx=;
6) [formula] int sin^3xcos^3xdx =;
7) [formula] int (x+2)3^xdx =
Очень,очень буду благодарна!!!
2) [formula] int sin 7*xdx =;
3) [formula] int tg^7xdx =;
4) [formula] int {-1}{-2/3}{dx/(3x+1)^5} =;
5) [formula] int (x + 1)In2xdx=;
6) [formula] int sin^3xcos^3xdx =;
7) [formula] int (x+2)3^xdx =
Очень,очень буду благодарна!!!
Обсуждение
09.04.2012, 20:15
общий
это ответ
Здравствуйте, Посетитель - 393161!
1)
(почему косинус так интегрируется - см. следующий аналогичный пример с синусом).
2)
.
Замена
7x = y,
7dx = dy.
.
6)
.
Делаем замену
,
.
.
1)
(почему косинус так интегрируется - см. следующий аналогичный пример с синусом).
2)
.Замена
7x = y,
7dx = dy.
.6)
.Делаем замену
,..
09.04.2012, 21:24
общий
это ответ
Здравствуйте, Посетитель - 393161!
3) делаем замену u=cos x:
[$8747$]tg7xdx=[$8747$]sin7xdx/cos7x=[$8747$]sin6x*sin xdx/cos7x=
=-[$8747$](1-cos2x)3d(cos x)/cos7x=-[$8747$](1-u2)3du/u7=
=-[$8747$](1-3u2+3u4-u60du/u7=-[$8747$](u-7-3u-5+3u-3-u-1)du=
=(u-6/6)-3(u-4/4)+3(u-2/2)+ln|u|+C=
=(1/(6cos6x))-(3/(4cos4x))+(3/(2cos2x))+ln|cos x|+C
7) интегрируем по частям
[$8747$](x+2)3xdx=[$8747$](x+2)d(3x/ln3)=(x+2)3x/ln3-(1/ln3)[$8747$]3xdx=
=(x+2)3x/ln3-3x/ln23+C
3) делаем замену u=cos x:
[$8747$]tg7xdx=[$8747$]sin7xdx/cos7x=[$8747$]sin6x*sin xdx/cos7x=
=-[$8747$](1-cos2x)3d(cos x)/cos7x=-[$8747$](1-u2)3du/u7=
=-[$8747$](1-3u2+3u4-u60du/u7=-[$8747$](u-7-3u-5+3u-3-u-1)du=
=(u-6/6)-3(u-4/4)+3(u-2/2)+ln|u|+C=
=(1/(6cos6x))-(3/(4cos4x))+(3/(2cos2x))+ln|cos x|+C
7) интегрируем по частям
[$8747$](x+2)3xdx=[$8747$](x+2)d(3x/ln3)=(x+2)3x/ln3-(1/ln3)[$8747$]3xdx=
=(x+2)3x/ln3-3x/ln23+C
5
09.04.2012, 21:53
общий
это ответ
Здравствуйте, Посетитель - 393161!
4.
С уважением.
4.
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
09.04.2012, 21:59
общий
это ответ
Здравствуйте, Посетитель - 393161!
5) Используем формулу интегрирования по частям: [$8747$]udv=uv-[$8747$]vdu.
Обозначим u=ln2x, dv=(x+1)dx; тогда du=(ln2x)'dx=1/x[$149$]dx, v=[$8747$](x+1)dx=x2/2+x.
Подставив в формулу, получим
[$8747$](x+1)ln2xdx=(x2/2+x)ln2x-[$8747$](x/2+1)dx=(x2/2+x)ln2x-x2/4-x+C.
5) Используем формулу интегрирования по частям: [$8747$]udv=uv-[$8747$]vdu.
Обозначим u=ln2x, dv=(x+1)dx; тогда du=(ln2x)'dx=1/x[$149$]dx, v=[$8747$](x+1)dx=x2/2+x.
Подставив в формулу, получим
[$8747$](x+1)ln2xdx=(x2/2+x)ln2x-[$8747$](x/2+1)dx=(x2/2+x)ln2x-x2/4-x+C.
5
Форма ответа
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