Question

Найти Интеграл х^2dx/(x^3+1)^2

Answer 1

$\int \frac{x^2\, dx}{(x^3+1)^2}=[\; t=x^3+1\; ,\; dt=3x^2\, dx\; ]=\frac{1}{3}\int \frac{dt}{t^2}=\frac{1}{3}\cdot (-\frac{1}{t})+C=\\\\=-\frac{1}{3\, (x^3+1)^2}+C$