Интеграл (x^2) \(x^2+4) dx

Question

Интеграл (x^2) \(x^2+4) dx

Answer 1

∫ x^2/(x^2+4)dx = ∫ (x^2+4)/(x^2+4)dx - 4∫ (1/(x^2+4)dx =
 = x - 4(1/2*arctg(x/2) + C  = x - 2arctg(x/2) + C
т.к. ∫ (1/(x^2+a^2) = (1/a)*arctg(x/a) + C