1) ∫ (14x^6 - 4 - 5/x^4)dx = 2x^7 - 4x + 5/x^3 + C2) ∫ (7x^6 + 12 - 2/x)dx = (7/7)x^7 + 12x - 2ln|x| + C3) ∫ (35x^4 + 4 - 4/x)dx = 7x^5 + 4x - 4ln|x| + C4) ∫ (10x^4 + 5 - 5/x^6)dx = 2x^5 + 5x + 5/x^5 + C
Неопределенные функции:1) y = (5x + 10)/(2x - 4) = (5/2) + 20/(2x - 4)2) y = (3 - 2x^2) / (6 - 3x^2) = (3 - 2x^2) / 3(2 - x^2) = -(2x^2 - 3) / (x^2 - 2) = -2 + 1 / (x^2 - 2)3) y = (2 - x) / (3x + 5) = (2 - x) / (3x + 5)4) y = (2x^2 + 4) / (1 - x^2) = -2(x^2 - 1) + 6 / (x^2 - 1) = -2 + 6 / (x^2 - 1)
1) ∫ (14x^6 - 4 - 5/x^4)dx = 2x^7 - 4x + 5/x^3 + C
2) ∫ (7x^6 + 12 - 2/x)dx = (7/7)x^7 + 12x - 2ln|x| + C
3) ∫ (35x^4 + 4 - 4/x)dx = 7x^5 + 4x - 4ln|x| + C
4) ∫ (10x^4 + 5 - 5/x^6)dx = 2x^5 + 5x + 5/x^5 + C
Неопределенные функции:
1) y = (5x + 10)/(2x - 4) = (5/2) + 20/(2x - 4)
2) y = (3 - 2x^2) / (6 - 3x^2) = (3 - 2x^2) / 3(2 - x^2) = -(2x^2 - 3) / (x^2 - 2) = -2 + 1 / (x^2 - 2)
3) y = (2 - x) / (3x + 5) = (2 - x) / (3x + 5)
4) y = (2x^2 + 4) / (1 - x^2) = -2(x^2 - 1) + 6 / (x^2 - 1) = -2 + 6 / (x^2 - 1)