Помогите, пожалуйста, решить интегралы:
1) int x * arctg x dx
2) int dx/(x^2 - 2x + 3)^(1/2)

1) int x * arctg x dx = int arctg x d(1/2 * x^2) = 1/2 * int arctg x d(x^2) =
= 1/2 * x^2 * arctg x - 1/2 * int x^2 d(arctg x) =
= 1/2 * x^2 * arctg x - 1/2 * int x^2/(1 + x^2) dx =
= 1/2 * x^2 * arctg x - 1/2 * int (1 + x^2 - 1)/(1 + x^2) dx =
= 1/2 * x^2 * arctg x - 1/2 * int dx + 1/2 * int dx/(1 + x^2) =
= 1/2 * x^2 * arctg x - 1/2 * x + 1/2 * arctg x + C =
= 1/2 * (x^2 + 1) * arctg x - 1/2 * x + C
2) int dx/(x^2 - 2x + 3)^(1/2) = int dx/((x - 1)^2 + 2)^(1/2) =
= ln |x - 1 + ((x - 1)^2 + 2)^(1/2)| + C = ln |x - 1 + (x^2 - 2x + 3)^(1/2)| + C