Помогите, пожалуйста, найти интеграл
int (ln x)^2 dx
int (ln x)^2 dx = x * (ln x)^2 - int x d((ln x)^2) =
= x * (ln x)^2 - int x * 2 * ln x * (ln x)' dx =
= x * (ln x)^2 - int x * 2 * ln x * 1/x dx =
= x * (ln x)^2 - 2 * int ln x dx =
= x * (ln x)^2 - 2 * x * ln x + 2 * int x d(ln x) =
= x * (ln x)^2 - 2 * x * ln x + 2 * int x * 1/x dx =
= x * (ln x)^2 - 2 * x * ln x + 2 * int dx =
= x * (ln x)^2 - 2 * x * ln x + 2 * x + C
Спасибо!
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