Задача №1298
Условие
Найти интеграл \(\int\frac{x^2dx}{x^3+1}\).
Решение
\[
\int\frac{x^2dx}{x^3+1}
=\left[\begin{aligned}& d\left(x^3+1\right)=3x^2dx;\\& x^2dx=\frac{1}{3}d\left(x^3+1\right).\end{aligned}\right]
=\frac{1}{3}\int\frac{d\left(x^3+1\right)}{x^3+1}
=\frac{1}{3}\ln\left|x^3+1\right|+C
=\frac{\ln\left|x^3+1\right|}{3}+C
\]
Ответ:
\(\frac{\ln\left|x^3+1\right|}{3}+C\)