∫ dx/[(x + 1)(x + 3)]
= (1/2)∫ [(x + 3) - (x + 1)]/[(x + 1)(x + 3)] dx
= (1/2)∫ [1/(x + 1) - 1/(x + 3)] dx
= (1/2)[ln| x + 1 | - ln| x + 3 |] + C
= (1/2)ln| (x + 1)/(x + 3) | + C
= ln√[(x + 1)/(x + 3)] + C