Question

integration of dx/(x+1)(x+3)

Answer 1

Here use the method of partial fraction.
$\frac{dx}{(x + 1)(x + 3)} = \frac{a}{(x + 1)} + \frac{b}{(x + 3)}$
1=a(x+3)+b((x+1)

put x=-1

a=1/2

put x=-3
b=-1/2

now put a and b in eq. 1
$\frac{dx}{(x + 1)(x + 3)} = \frac{1}{2(x + 1)} - \frac{1}{2(x + 3)} \\ simply \: integrate \: then... \\ = \frac{1}{2} ln(x + 1) - \frac{1}{2} ln(x + 3)$
hope it will help you.