Помогите, пожалуйста, вычислить интеграл
int (4 9) x^(1/2)/(x^(1/2) - 1) dx

int (4 9) x^(1/2)/(x^(1/2) - 1) dx = | x^(1/2) = t, x = t^2, dx = 2 * t dt | =
= int (2 3) t/(t - 1) * 2 * t dt = 2 * int (2 3) t^2/(t - 1) dt =
= 2 * int (2 3) (t^2 - t + t - 1 + 1)/(t - 1) dt =
= 2 * int (2 3) (t * (t - 1) + (t - 1) + 1)/(t - 1) dt =
= 2 * int (2 3) t dt + 2 * int (2 3) dt + 2 * int (2 3) 1/(t - 1) dt =
= 2 * (1/2 * t^2)_{2}^{3} + 2 * (t)_{2}^{3} + 2 * (ln |t - 1|)_{2}^{3} =
= 2 * (1/2 * 3^2 - 1/2 * 2^2) + 2 * (3 - 2) + 2 * (ln 2 - ln 1) =
= 2 * (9/2 - 2) + 2 + 2 * ln 2 = 9 - 4 + 2 + 2 * ln 2 = 7 + 2 * ln 2