int ln (x^2 + 4) dx = x * ln (x^2 + 4) - int x d(ln (x^2 + 4)) =
= x * ln (x^2 + 4) - int x * (ln (x^2 + 4))' dx =
= x * ln (x^2 + 4) - int x * 1/(x^2 + 4) * (x^2 + 4)' dx =
= x * ln (x^2 + 4) - int x * 1/(x^2 + 4) * 2x dx =
= x * ln (x^2 + 4) - int 2 * x^2/(x^2 + 4) dx =
= x * ln (x^2 + 4) - 2 * int x^2/(x^2 + 4) dx =
= x * ln (x^2 + 4) - 2 * int (x^2 + 4 - 4)/(x^2 + 4) dx =
= x * ln (x^2 + 4) - 2 * int dx + 8 * int dx/(x^2 + 4) =
= x * ln (x^2 + 4) - 2 * x + 8 * 1/2 * arctg (x/2) + C =
= x * ln (x^2 + 4) - 2 * x + 4 * arctg (x/2) + C