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Консультация № 109301
13.11.2007, 22:52
0.00 руб.
0
2
2
Решите пожалуйста любой из этих примеров с интеграллами:
1.⌠7dx/3x^3 sqrt(ln x);
2.⌠x-3/3x+1 dx;
3.⌠2x^4dx/sqrt(4-x^10);
4.⌠2x^2+x+4/x^3+x^2+4x+4 dx
1.⌠7dx/3x^3 sqrt(ln x);
2.⌠x-3/3x+1 dx;
3.⌠2x^4dx/sqrt(4-x^10);
4.⌠2x^2+x+4/x^3+x^2+4x+4 dx
Обсуждение
Неизвестный
13.11.2007, 23:01
общий
это ответ
Здравствуйте, Курилов Олег Олегович!
4) ⌠2x^2+x+4/x^3+x^2+4x+4 dx=⌠3x^2+2x+4/x^3+x^2+4x+4 dx-
-⌠(x^2+x)/x^3+x^2+4x+4 dx =
=ln(x^3+x^2+4x+4)-⌠x/(x^2+4) dx=
=ln(x^3+x^2+4x+4)-1/2 ln(x^2+4)+c
4) ⌠2x^2+x+4/x^3+x^2+4x+4 dx=⌠3x^2+2x+4/x^3+x^2+4x+4 dx-
-⌠(x^2+x)/x^3+x^2+4x+4 dx =
=ln(x^3+x^2+4x+4)-⌠x/(x^2+4) dx=
=ln(x^3+x^2+4x+4)-1/2 ln(x^2+4)+c
Неизвестный
13.11.2007, 23:02
общий
это ответ
Здравствуйте, Курилов Олег Олегович!
2.
∫(x-3)dx/(3x+1) = ∫(1/3 – (10/3)/(3x+1))dx = 1/3*∫dx – 10/3*∫dx/(3x+1) = x/3 – 10/9*∫d(3x+1)/(3x+1) = x/3 – 10/9*ln|3x+1| + C.
3.
∫2x<sup>4</sup>dx/sqrt(4-x<sup>10</sup>) = ∫x<sup>4</sup>dx/sqrt(1-x<sup>10</sup>/4) = {t = x<sup>5</sup>/2, dt = 5x<sup>4</sup>dx/2} = 2/5 * ∫dt/sqrt(1-t²) = 2/5*arcsin(t) + C = 2/5*arcsin(x<sup>5</sup>/2) + C.
2.
∫(x-3)dx/(3x+1) = ∫(1/3 – (10/3)/(3x+1))dx = 1/3*∫dx – 10/3*∫dx/(3x+1) = x/3 – 10/9*∫d(3x+1)/(3x+1) = x/3 – 10/9*ln|3x+1| + C.
3.
∫2x<sup>4</sup>dx/sqrt(4-x<sup>10</sup>) = ∫x<sup>4</sup>dx/sqrt(1-x<sup>10</sup>/4) = {t = x<sup>5</sup>/2, dt = 5x<sup>4</sup>dx/2} = 2/5 * ∫dt/sqrt(1-t²) = 2/5*arcsin(t) + C = 2/5*arcsin(x<sup>5</sup>/2) + C.
Форма ответа
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