ИНТЕГРАЛЫ: 1) (3x^2 - 2radic;x + 4x - 5) dx 2) radic;(1 - x) dx 3) ctg3x dx 4) x^2 dx/ (x^3 - 1)^2

Question

ИНТЕГРАЛЫ: 1) (3x^2 - 2radic;x + 4x - 5) dx 2) radic;(1 - x) dx 3) ctg3x dx 4) x^2 dx/ (x^3 - 1)^2

Алгебра

ИНТЕГРАЛЫ: 1) (3x^2 - 2√x + 4x - 5) dx 2) √(1 - x) dx 3) ctg3x dx 4) x^2 dx/ (x^3 - 1)^2

Гость

Ответ(ы) на вопрос:

Accepted Answer

1. S(3x^2 - 2sqrt(x) + 4x - 5)dx = 3x^3/3 - 2 x^(3/2) * 2/3 + 4x^2/2- 5x + c = x^3 - 4/3 * x^(3/2) + 2x^2 - 5x + c 2. S(sqrt(1-x))dx = -S(sqrt(1-x))d(1-x) = - (1-x)^(3/2) * 2/3 + c = -2/3 (1-x)^(3/2)+c 3. S ctg3x dx = 1/3 S(cos3x/sin3x) d(3x) = 1/3 S 1/sin3x d(sin3x) = 1/3 ln(sin3x) + c 4. S x^2 / (x^3-1)^2 dx = 1/3 S 1/(x^3-1)^2 d(x^3-1) = -1/3 (x^3-1)^(-1)+c = -1/3 * 1/(x^3-1) + c