Каким способом и как решить int (0 1) (1 + x^2) dx/(x^3 + 3х + 1)^2
Подскажите пожалуйста.
int (0 1) (1 + x^2) dx/(x^3 + 3х + 1)^2 = int (0 1) d(x + x^3/3)/(x^3 + 3x + 1)^2 =
= 1/3 * int (0 1) d(x^3 + 3x)/(x^3 + 3x + 1)^2 =
= 1/3 * int (0 1) d(x^3 + 3x + 1)/(x^3 + 3x + 1)^2 =
= | t = x^3 + 3x + 1 | = 1/3 * int (1 5) dt/t^2 = 1/3 * (-1/t)_{1}^{5} =
= 1/3 * (-1/5 + 1/1) = 1/3 * (1 - 1/5) = 1/3 * 4/5 = 4/15
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